Sequences & Patterns · MCQ assessment

Version A

Tick one box (A, B, C or D) for each question. 15 questions, 1 mark each.Name: __________ Class: ______

Mark bar · shade a box for each question you got right

123456789101112131415

/ 15

1Here are the first four terms of a sequence.
$46,\ 44,\ 42,\ 40$
Write down the next two terms of the sequence.

A38, 36B36, 34C42, 40D80, 78

2Here is a sequence.
$1,\ 4,\ 16,\ 64$
Write down the term-to-term rule for this sequence.

Amultiply by 3Bmultiply by 4Cmultiply by 5Dadd 3

3Here are the first four terms of a sequence.
$11,\ 3,\ -5,\ -13$
Work out the next two terms.

A-21, -29B-22, -31C21, 29D-5, 3

4Here is a sequence with one term missing.
$43,\ \boxed{\phantom{00}},\ 35,\ 31,\ 27$
Work out the value of the missing term.

A38B39C35D43

5Here are some consecutive terms of a well-known sequence.
$3,\ 6,\ 10,\ 15,\ 21$
Write down the next two terms.

A28, 36B36, 28C27, 33D343, 512

6The $n$th term of a sequence is $n^2 + 2$.
Work out the smallest integer $n$ for which the $n$th term is greater than $500$.

A24B25C23D22

7A list is made of $n$ consecutive whole numbers (for example $3, 4, 5, 6, 7, 8$ is a list of $6$ of them).
Write an expression, in terms of $n$, for the range of a list of $n$ consecutive whole numbers.

A2n - 1Bn - 1CnDn + 1

8Each term of this Fibonacci-type sequence is the sum of the two terms before it.
$2,\ 4,\ 6,\ \boxed{\phantom{0}},\ 16$
Work out the missing term.

A22B11C10D16

9In this number chain the same two steps repeat: “$\times 4$ then $-2$”, then “$+2$”, alternating.
The chain so far is:
$3, \; 10, \; 12, \; 46, \; 48, \; \boxed{?}$
The next step is “$\times 4$ then $-2$”.
Work out the next number in the chain.

A190B192C188D50

10Aisha says that $78$ is a triangular number.
Is Aisha correct? You must give a reason.

AIt cannot be decided without a calculatorBYes, it is a triangular numberCNo, it is not a triangular numberDYes, but only because it is even

11The 1st term of an arithmetic sequence is $3$ and the 4th term is $12$.
The same amount is added or subtracted each time.
Find the term-to-term rule.

Aadd 3Badd 4Cadd 9Dsubtract 3

12The first three terms of a sequence are
$s,\ t,\ st,\ \ldots$
Each term after the first two is the product of the two terms before it.
Find the 6th term, in terms of $s$ and $t$.

A$s^3t^5$B$s^2t^3$C$s^5t^3$D$s^2t^4$

13The first three terms of a Fibonacci-type sequence are $a$, $b$ and $a+b$.
Each term after the first two is the sum of the two terms before it.
The sequence begins
$a,\ b,\ a+b,\ \ldots$
Find the 7th term, in terms of $a$ and $b$.

A$3a+5b$B$5a+8b$C$8a+5b$D$5a+7b$

14The population of a town is modelled by $P_{n+1} = a\,P_n + 1000$, where $P_n$ is the population at the start of year $n$.
At the start of year 1 the population is $30000$, and at the start of year 2 it is $37000$.
Use the model to work out the population at the start of year 4.

A67576B55480C45400D54480

15The first three terms of a sequence are
$p,\ q,\ pq,\ \ldots$
Each term after the first two is the product of the two terms before it.
Find the 6th term, in terms of $p$ and $q$.

A$p^2q^4$B$p^5q^3$C$p^3q^5$D$p^2q^3$

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Sequences & Patterns · MCQ assessment

Version B

Tick one box (A, B, C or D) for each question. 15 questions, 1 mark each.Name: __________ Class: ______

Mark bar · shade a box for each question you got right

123456789101112131415

/ 15

1Here are the first four terms of a sequence.
$2,\ 12,\ 22,\ 32$
Write down the next two terms of the sequence.

A22, 32B52, 62C64, 74D42, 52

2A growing pattern uses square tiles.
Pattern 1 uses $6$ square tiles, Pattern 2 uses $10$ and Pattern 3 uses $14$.
How many more square tiles are needed to go from one pattern to the next?

A4B5C2D14

3Here are the first four terms of a sequence.
$7,\ 3,\ -1,\ -5$
Work out the next two terms.

A-1, 3B-10, -15C-9, -13D9, 13

4Here is a sequence with one term missing.
$3,\ 6,\ 12,\ \boxed{\phantom{00}},\ 48$
Work out the value of the missing term.

A24B31C26D22

5Here are some consecutive terms of a well-known sequence.
$16,\ 25,\ 36,\ 49$
Write down the next two terms.

A81, 64B36, 45C64, 81D62, 75

6The $n$th term of a sequence is $n^2 + 1$.
Work out the smallest integer $n$ for which the $n$th term is greater than $600$.

A24B25C27D26

7Each term of this Fibonacci-type sequence is the sum of the two terms before it.
$1,\ 7,\ 8,\ \boxed{\phantom{0}},\ 23$
Work out the missing term.

A31B16C23D15

8In this number chain the same two steps repeat: “$\times 3$ then $-2$”, then “$+2$”, alternating.
The chain so far is:
$4, \; 10, \; 12, \; 34, \; 36, \; \boxed{?}$
The next step is “$\times 3$ then $-2$”.
Work out the next number in the chain.

A108B38C104D106

9Priya says that $37$ is a triangular number.
Is Priya correct? You must give a reason.

AYes, it is a triangular numberBIt cannot be decided without a calculatorCNo, but only because it is oddDNo, it is not a triangular number

10In this sequence, each term after the second is the sum of the two terms before it.
The 1st, 3rd, 4th and 5th terms are
$2, \; \boxed{?}, \; 5, \; 8, \; 13$
Work out the missing 2nd term.

A5B2C3D7

11The 1st term of an arithmetic sequence is $38$ and the 4th term is $29$.
The same amount is added or subtracted each time.
Find the term-to-term rule.

Asubtract 4Bsubtract 3Csubtract 9Dadd 3

12The population of a town is modelled by $P_{n+1} = a\,P_n + 500$, where $P_n$ is the population at the start of year $n$.
At the start of year 1 the population is $30000$, and at the start of year 2 it is $33500$.
Use the model to work out the population at the start of year 4.

A41085B37350C41585D46244

13The first three terms of a Fibonacci-type sequence are $a$, $b$ and $a+b$.
Each term after the first two is the sum of the two terms before it.
The sequence begins
$a,\ b,\ a+b,\ a+2b,\ \ldots$
Find the 8th term, in terms of $a$ and $b$.

A$8a+12b$B$8a+13b$C$13a+8b$D$5a+8b$

14The first three terms of a sequence are
$s,\ t,\ st,\ \ldots$
Each term after the first two is the product of the two terms before it.
Find the 5th term, in terms of $s$ and $t$.

A$st^2$B$s^3t^2$C$s^2t^2$D$s^2t^3$

15The population of a town is modelled by $P_{n+1} = a\,P_n + 800$, where $P_n$ is the population at the start of year $n$.
At the start of year 1 the population is $25000$, and at the start of year 2 it is $30800$.
Use the model to work out the population at the start of year 4.

A37760B56134C46112D45312

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Sequences & Patterns · MCQ assessment

Version C

Tick one box (A, B, C or D) for each question. 15 questions, 1 mark each.Name: __________ Class: ______

Mark bar · shade a box for each question you got right

123456789101112131415

/ 15

1Here is a sequence.
$1,\ 3,\ 9,\ 27$
Write down the term-to-term rule for this sequence.

Aadd 2Bmultiply by 4Cmultiply by 2Dmultiply by 3

2In a Fibonacci-type sequence, each term is the sum of the two terms before it.
Here are the first four terms of such a sequence.
$3,\ 6,\ 9,\ 15$
Write down the next two terms.

A16, 25B24, 63C24, 39D30, 54

3Here is a sequence with one term missing.
$9,\ 16,\ 23,\ \boxed{\phantom{00}},\ 37$
Work out the value of the missing term.

A30B37C31D23

4Here is a sequence.
$1,\ 8,\ 27,\ 64$
Choose the name of this type of sequence.

AEven numbersBCube numbersCTriangular numbersDSquare numbers

5Here are some consecutive terms of a well-known sequence.
$16,\ 25,\ 36,\ 49$
Write down the next two terms.

A81, 64B64, 81C62, 75D36, 45

6The $n$th term of a sequence is $n^2 + 5$.
Work out the smallest integer $n$ for which the $n$th term is greater than $300$.

A18B17C20D19

7In this number chain the same two steps repeat: “$\times 4$ then $-2$”, then “$+2$”, alternating.
The chain so far is:
$2, \; 6, \; 8, \; 30, \; 32, \; \boxed{?}$
The next step is “$\times 4$ then $-2$”.
Work out the next number in the chain.

A128B124C126D34

8The 1st term of an arithmetic sequence is $4$ and the 4th term is $13$.
The same amount is added or subtracted each time.
Find the term-to-term rule.

Asubtract 3Badd 9Cadd 4Dadd 3

9In this sequence, each term after the second is the sum of the two terms before it.
The 1st, 3rd, 4th and 5th terms are
$2, \; \boxed{?}, \; 11, \; 20, \; 31$
Work out the missing 2nd term.

A2B11C13D9

10A list is made of $n$ consecutive whole numbers (for example $5, 6, 7, 8, 9, 10, 11$ is a list of $7$ of them).
Write an expression, in terms of $n$, for the range of a list of $n$ consecutive whole numbers.

A2n - 1Bn - 1Cn + 1Dn

11Priya says that $36$ is a square number.
Is Priya correct? You must give a reason.

AYes, it is a square numberBYes, but only because it is evenCIt cannot be decided without a calculatorDNo, it is not a square number

12The first three terms of a Fibonacci-type sequence are $a$, $b$ and $a+b$.
Each term after the first two is the sum of the two terms before it.
The sequence begins
$a,\ b,\ a+b,\ \ldots$
Find the 8th term, in terms of $a$ and $b$.

A$8a+13b$B$13a+8b$C$5a+8b$D$8a+12b$

13The first three terms of a sequence are
$p,\ q,\ pq,\ \ldots$
Each term after the first two is the product of the two terms before it.
Find the 6th term, in terms of $p$ and $q$.

A$p^2q^3$B$p^3q^5$C$p^2q^4$D$p^5q^3$

14The population of a town is modelled by $P_{n+1} = a\,P_n + 1000$, where $P_n$ is the population at the start of year $n$.
At the start of year 1 the population is $40000$, and at the start of year 2 it is $49000$.
Use the model to work out the population at the start of year 4.

A88312B71760C59800D72760

15The first three terms of a Fibonacci-type sequence are $a$, $b$ and $a+b$.
Each term after the first two is the sum of the two terms before it.
The sequence begins
$a,\ b,\ a+b,\ a+2b,\ \ldots$
Find the 7th term, in terms of $a$ and $b$.

A$5a+8b$B$3a+5b$C$8a+5b$D$5a+7b$

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Sequences & Patterns · MCQ assessment

Version D

Tick one box (A, B, C or D) for each question. 15 questions, 1 mark each.Name: __________ Class: ______

Mark bar · shade a box for each question you got right

123456789101112131415

/ 15

1A growing pattern uses counters.
Pattern 1 uses $10$ counters, Pattern 2 uses $16$ and Pattern 3 uses $22$.
How many more counters are needed to go from one pattern to the next?

A22B6C7D4

2In a Fibonacci-type sequence, each term is the sum of the two terms before it.
Here are the first four terms of such a sequence.
$1,\ 2,\ 3,\ 5$
Write down the next two terms.

A8, 21B6, 9C8, 13D10, 18

3Here is a sequence with one term missing.
$41,\ 35,\ 29,\ \boxed{\phantom{00}},\ 17$
Work out the value of the missing term.

A17B22C29D23

4Here are the first four terms of a sequence.
$10,\ 2,\ -6,\ -14$
Work out the next two terms.

A-22, -30B22, 30C-23, -32D-6, 2

5A pattern is made from tiles.
Pattern 1 uses $3$ tiles, Pattern 2 uses $5$, Pattern 3 uses $7$ and Pattern 4 uses $9$.
How many tiles are used in Pattern 10?

A23B20C19D21

6In this number chain the same two steps repeat: “$\times 2$ then $-2$”, then “$+2$”, alternating.
The chain so far is:
$5, \; 8, \; 10, \; 18, \; 20, \; \boxed{?}$
The next step is “$\times 2$ then $-2$”.
Work out the next number in the chain.

A40B38C36D22

7Jack says that $49$ is a square number.
Is Jack correct? You must give a reason.

AYes, but only because it is evenBNo, it is not a square numberCYes, it is a square numberDIt cannot be decided without a calculator

8Each term of this Fibonacci-type sequence is the sum of the two terms before it.
$5,\ 6,\ \boxed{\phantom{0}},\ 17,\ 28$
Work out the missing term.

A12B11C17D23

9The $n$th term of a sequence is $n^2 + 3$.
Work out the smallest integer $n$ for which the $n$th term is greater than $700$.

A29B28C26D27

10In this sequence, each term after the second is the sum of the two terms before it.
The 1st, 3rd, 4th and 5th terms are
$6, \; \boxed{?}, \; 16, \; 26, \; 42$
Work out the missing 2nd term.

A10B22C16D6

11A list is made of $n$ consecutive whole numbers (for example $7, 8, 9, 10, 11, 12$ is a list of $6$ of them).
Write an expression, in terms of $n$, for the range of a list of $n$ consecutive whole numbers.

An + 1BnC2n - 1Dn - 1

12The first three terms of a sequence are
$m,\ n,\ mn,\ \ldots$
Each term after the first two is the product of the two terms before it.
Find the 6th term, in terms of $m$ and $n$.

A$m^2n^4$B$m^5n^3$C$m^2n^3$D$m^3n^5$

A$8a+13b$B$8a+12b$C$13a+8b$D$5a+8b$

14The population of a town is modelled by $P_{n+1} = a\,P_n + 500$, where $P_n$ is the population at the start of year $n$.
At the start of year 1 the population is $40000$, and at the start of year 2 it is $48500$.
Use the model to work out the population at the start of year 4.

A70440B58700C70940D85628

15The first three terms of a sequence are
$x,\ y,\ xy,\ \ldots$
Each term after the first two is the product of the two terms before it.
Find the 5th term, in terms of $x$ and $y$.

A$x^2y^3$B$x^2y^2$C$x^3y^2$D$xy^2$

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Sequences & Patterns · MCQ assessment

Version E

Tick one box (A, B, C or D) for each question. 15 questions, 1 mark each.Name: __________ Class: ______

Mark bar · shade a box for each question you got right

123456789101112131415

/ 15

1Here is a sequence.
$8,\ 12,\ 16,\ 20$
Write down the term-to-term rule for this sequence.

Asubtract 4Bmultiply by 4Cadd 5Dadd 4

2A growing pattern uses square tiles.
Pattern 1 uses $7$ square tiles, Pattern 2 uses $12$ and Pattern 3 uses $17$.
How many more square tiles are needed to go from one pattern to the next?

A5B6C2D17

3A pattern is made from counters.
Pattern 1 uses $7$ counters, Pattern 2 uses $12$, Pattern 3 uses $17$ and Pattern 4 uses $22$.
How many counters are used in Pattern 7?

A32B42C37D35

4Here are the first terms of a well-known sequence.
$1,\ 4,\ 9,\ 16$
Write down the next two terms.

A36, 25B23, 30C25, 36D125, 216

5In a Fibonacci-type sequence, each term is the sum of the two terms before it.
Here are the first four terms of such a sequence.
$5,\ 2,\ 7,\ 9$
Write down the next two terms.

A16, 41B18, 34C10, 17D16, 25

6The 1st term of an arithmetic sequence is $10$ and the 4th term is $28$.
The same amount is added or subtracted each time.
Find the term-to-term rule.

Aadd 18Badd 7Csubtract 6Dadd 6

7Each term of this Fibonacci-type sequence is the sum of the two terms before it.
$1,\ 6,\ 7,\ \boxed{\phantom{0}},\ 20$
Work out the missing term.

A13B27C14D20

8In this sequence, each term after the second is the sum of the two terms before it.
The 1st, 3rd, 4th and 5th terms are
$5, \; \boxed{?}, \; 11, \; 17, \; 28$
Work out the missing 2nd term.

A11B5C16D6

9A list is made of $n$ consecutive whole numbers (for example $3, 4, 5, 6, 7, 8$ is a list of $6$ of them).
Write an expression, in terms of $n$, for the range of a list of $n$ consecutive whole numbers.

AnBn + 1Cn - 1D2n - 1

10In this number chain the same two steps repeat: “$\times 3$ then $-2$”, then “$+2$”, alternating.
The chain so far is:
$4, \; 10, \; 12, \; 34, \; 36, \; \boxed{?}$
The next step is “$\times 3$ then $-2$”.
Work out the next number in the chain.

A108B106C104D38

11Maya says that $147$ is a square number.
Is Maya correct? You must give a reason.

AYes, it is a square numberBNo, but only because it is oddCIt cannot be decided without a calculatorDNo, it is not a square number

12The first three terms of a sequence are
$m,\ n,\ mn,\ \ldots$
Each term after the first two is the product of the two terms before it.
Find the 6th term, in terms of $m$ and $n$.

A$m^2n^4$B$m^5n^3$C$m^2n^3$D$m^3n^5$

13The population of a town is modelled by $P_{n+1} = a\,P_n + 500$, where $P_n$ is the population at the start of year $n$.
At the start of year 1 the population is $30000$, and at the start of year 2 it is $36500$.
Use the model to work out the population at the start of year 4.

A53160B44300C64892D53660

14The first three terms of a Fibonacci-type sequence are $a$, $b$ and $a+b$.
Each term after the first two is the sum of the two terms before it.
The sequence begins
$a,\ b,\ a+b,\ a+2b,\ 2a+3b,\ \ldots$
Find the 7th term, in terms of $a$ and $b$.

A$5a+7b$B$8a+5b$C$5a+8b$D$3a+5b$

15The first three terms of a sequence are
$x,\ y,\ xy,\ \ldots$
Each term after the first two is the product of the two terms before it.
Find the 5th term, in terms of $x$ and $y$.

A$x^3y^2$B$x^2y^3$C$x^2y^2$D$xy^2$

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Sequences & Patterns · MCQ assessment

Version F

Tick one box (A, B, C or D) for each question. 15 questions, 1 mark each.Name: __________ Class: ______

Mark bar · shade a box for each question you got right

123456789101112131415

/ 15

1Here is a sequence.
$2,\ 4,\ 8,\ 16$
Write down the term-to-term rule for this sequence.

Amultiply by 2Bmultiply by 1Cadd 2Dmultiply by 3

2Here are the first four terms of a sequence.
$48,\ 41,\ 34,\ 27$
Write down the next two terms of the sequence.

A34, 27B13, 6C54, 47D20, 13

3In a Fibonacci-type sequence, each term is the sum of the two terms before it.
Here are the first four terms of such a sequence.
$5,\ 3,\ 8,\ 11$
Write down the next two terms.

A19, 49B12, 20C19, 30D22, 41

4A pattern is made from tiles.
Pattern 1 uses $6$ tiles, Pattern 2 uses $10$, Pattern 3 uses $14$ and Pattern 4 uses $18$.
How many tiles are used in Pattern 7?

A28B26C30D34

5Here are some consecutive terms of a well-known sequence.
$27,\ 64,\ 125,\ 216$
Write down the next two terms.

A49, 64B343, 512C307, 398D512, 343

6A list is made of $n$ consecutive whole numbers (for example $4, 5, 6, 7, 8, 9, 10$ is a list of $7$ of them).
Write an expression, in terms of $n$, for the range of a list of $n$ consecutive whole numbers.

An + 1B2n - 1Cn - 1Dn

7The $n$th term of a sequence is $n^2 + 5$.
Work out the smallest integer $n$ for which the $n$th term is greater than $500$.

A22B24C23D25

8The 1st term of an arithmetic sequence is $29$ and the 4th term is $11$.
The same amount is added or subtracted each time.
Find the term-to-term rule.

Asubtract 18Bsubtract 7Cadd 6Dsubtract 6

9In this sequence, each term after the second is the sum of the two terms before it.
The 1st, 3rd, 4th and 5th terms are
$6, \; \boxed{?}, \; 18, \; 30, \; 48$
Work out the missing 2nd term.

A18B6C24D12

10In this number chain the same two steps repeat: “$\times 4$ then $-2$”, then “$+2$”, alternating.
The chain so far is:
$2, \; 6, \; 8, \; 30, \; 32, \; \boxed{?}$
The next step is “$\times 4$ then $-2$”.
Work out the next number in the chain.

A128B124C126D34

11Each term of this Fibonacci-type sequence is the sum of the two terms before it.
$2,\ 4,\ 6,\ \boxed{\phantom{0}},\ 16$
Work out the missing term.

A11B10C16D22

12The population of a town is modelled by $P_{n+1} = a\,P_n + 1000$, where $P_n$ is the population at the start of year $n$.
At the start of year 1 the population is $25000$, and at the start of year 2 it is $31000$.
Use the model to work out the population at the start of year 4.

A46840B45840C38200D57208

13The first three terms of a sequence are
$p,\ q,\ pq,\ \ldots$
Each term after the first two is the product of the two terms before it.
Find the 5th term, in terms of $p$ and $q$.

A$p^3q^2$B$p^2q^3$C$p^2q^2$D$pq^2$

14The first three terms of a Fibonacci-type sequence are $a$, $b$ and $a+b$.
Each term after the first two is the sum of the two terms before it.
The sequence begins
$a,\ b,\ a+b,\ \ldots$
Find the 8th term, in terms of $a$ and $b$.

A$8a+13b$B$8a+12b$C$13a+8b$D$5a+8b$

A46112B37760C45312D56134

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Sequences & Patterns · MCQ assessment

Version G

Tick one box (A, B, C or D) for each question. 15 questions, 1 mark each.Name: __________ Class: ______

Mark bar · shade a box for each question you got right

123456789101112131415

/ 15

1A growing pattern uses matchsticks.
Pattern 1 uses $5$ matchsticks, Pattern 2 uses $8$ and Pattern 3 uses $11$.
How many more matchsticks are needed to go from one pattern to the next?

A3B4C11D2

2Here are the first four terms of a sequence.
$6,\ 10,\ 14,\ 18$
Write down the next two terms of the sequence.

A22, 26B14, 18C26, 30D36, 40

3Here are the first four terms of a sequence.
$10,\ 2,\ -6,\ -14$
Work out the next two terms.

A-22, -30B22, 30C-23, -32D-6, 2

4In a Fibonacci-type sequence, each term is the sum of the two terms before it.
Here are the first four terms of such a sequence.
$5,\ 8,\ 13,\ 21$
Write down the next two terms.

A22, 35B34, 55C42, 76D34, 89

5Here is a sequence with one term missing.
$1,\ 6,\ \boxed{\phantom{00}},\ 16,\ 21$
Work out the value of the missing term.

A11B16C6D12

6Sam says that $91$ is a triangular number.
Is Sam correct? You must give a reason.

ANo, it is not a triangular numberBIt cannot be decided without a calculatorCYes, it is a triangular numberDYes, but only because it is even

7A list is made of $n$ consecutive whole numbers (for example $7, 8, 9, 10, 11, 12, 13, 14$ is a list of $8$ of them).
Write an expression, in terms of $n$, for the range of a list of $n$ consecutive whole numbers.

An + 1BnC2n - 1Dn - 1

8The 1st term of an arithmetic sequence is $50$ and the 4th term is $26$.
The same amount is added or subtracted each time.
Find the term-to-term rule.

Asubtract 6Bsubtract 8Csubtract 24Dadd 8

9In this number chain the same two steps repeat: “$\times 4$ then $-3$”, then “$+3$”, alternating.
The chain so far is:
$4, \; 13, \; 16, \; 61, \; 64, \; \boxed{?}$
The next step is “$\times 4$ then $-3$”.
Work out the next number in the chain.

A250B67C256D253

10In this sequence, each term after the second is the sum of the two terms before it.
The 1st, 3rd, 4th and 5th terms are
$3, \; \boxed{?}, \; 13, \; 23, \; 36$
Work out the missing 2nd term.

A10B3C16D13

11The $n$th term of a sequence is $n^2 + 4$.
Work out the smallest integer $n$ for which the $n$th term is greater than $250$.

A16B18C15D17

12The population of a town is modelled by $P_{n+1} = a\,P_n + 500$, where $P_n$ is the population at the start of year $n$.
At the start of year 1 the population is $25000$, and at the start of year 2 it is $30500$.
Use the model to work out the population at the start of year 4.

A44520B37100C45020D54524

13The first three terms of a sequence are
$a,\ b,\ ab,\ \ldots$
Each term after the first two is the product of the two terms before it.
Find the 6th term, in terms of $a$ and $b$.

A$a^5b^3$B$a^2b^4$C$a^2b^3$D$a^3b^5$

A$8a+12b$B$8a+13b$C$13a+8b$D$5a+8b$

15The population of a town is modelled by $P_{n+1} = a\,P_n + 800$, where $P_n$ is the population at the start of year $n$.
At the start of year 1 the population is $30000$, and at the start of year 2 it is $33800$.
Use the model to work out the population at the start of year 4.

A42578B41778C47636D37980

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Sequences & Patterns · MCQ assessment

Version H

Tick one box (A, B, C or D) for each question. 15 questions, 1 mark each.Name: __________ Class: ______

Mark bar · shade a box for each question you got right

123456789101112131415

/ 15

1Here is a sequence.
$4,\ 6,\ 8,\ 10$
Write down the term-to-term rule for this sequence.

Aadd 2Badd 3Csubtract 2Dmultiply by 2

2In a Fibonacci-type sequence, each term is the sum of the two terms before it.
Here are the first four terms of such a sequence.
$1,\ 6,\ 7,\ 13$
Write down the next two terms.

A20, 53B20, 33C26, 46D14, 21

3Here is a sequence with one term missing.
$3,\ 9,\ \boxed{\phantom{00}},\ 81,\ 243$
Work out the value of the missing term.

A46B24C27D30

4Here are the first four terms of a sequence.
$8,\ 3,\ -2,\ -7$
Work out the next two terms.

A-12, -17B-13, -19C12, 17D-2, 3

5Here are some consecutive terms of a well-known sequence.
$16,\ 25,\ 36,\ 49$
Write down the next two terms.

A81, 64B512, 729C64, 81D62, 75

6In this sequence, each term after the second is the sum of the two terms before it.
The 1st, 3rd, 4th and 5th terms are
$2, \; \boxed{?}, \; 8, \; 14, \; 22$
Work out the missing 2nd term.

A8B2C6D10

7In this number chain the same two steps repeat: “$\times 4$ then $-2$”, then “$+2$”, alternating.
The chain so far is:
$5, \; 18, \; 20, \; 78, \; 80, \; \boxed{?}$
The next step is “$\times 4$ then $-2$”.
Work out the next number in the chain.

A318B82C320D316

8The $n$th term of a sequence is $n^2 + 2$.
Work out the smallest integer $n$ for which the $n$th term is greater than $500$.

A22B23C24D25

9A list is made of $n$ consecutive whole numbers (for example $5, 6, 7, 8, 9, 10, 11, 12$ is a list of $8$ of them).
Write an expression, in terms of $n$, for the range of a list of $n$ consecutive whole numbers.

An - 1BnC2n - 1Dn + 1

10Each term of this Fibonacci-type sequence is the sum of the two terms before it.
$2,\ 3,\ 5,\ \boxed{\phantom{0}},\ 13$
Work out the missing term.

A13B18C8D9

11The 1st term of an arithmetic sequence is $36$ and the 4th term is $24$.
The same amount is added or subtracted each time.
Find the term-to-term rule.

Asubtract 3Bsubtract 12Csubtract 4Dadd 4

12The first three terms of a Fibonacci-type sequence are $a$, $b$ and $a+b$.
Each term after the first two is the sum of the two terms before it.
The sequence begins
$a,\ b,\ a+b,\ a+2b,\ \ldots$
Find the 7th term, in terms of $a$ and $b$.

A$3a+5b$B$5a+7b$C$8a+5b$D$5a+8b$

13The first three terms of a sequence are
$m,\ n,\ mn,\ \ldots$
Each term after the first two is the product of the two terms before it.
Find the 5th term, in terms of $m$ and $n$.

A$m^2n^3$B$m^2n^2$C$m^3n^2$D$mn^2$

A59800B88312C72760D71760

A$2a+3b$B$3a+4b$C$5a+3b$D$3a+5b$

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Sequences & Patterns · MCQ assessment

Version I

Tick one box (A, B, C or D) for each question. 15 questions, 1 mark each.Name: __________ Class: ______

Mark bar · shade a box for each question you got right

123456789101112131415

/ 15

1A growing pattern uses matchsticks.
Pattern 1 uses $6$ matchsticks, Pattern 2 uses $10$ and Pattern 3 uses $14$.
How many more matchsticks are needed to go from one pattern to the next?

A5B4C2D14

2Here is a sequence.
$8,\ 12,\ 16,\ 20$
Write down the term-to-term rule for this sequence.

Asubtract 4Bmultiply by 4Cadd 4Dadd 5

3Here is a sequence.
$4,\ 9,\ 16,\ 25,\ 36$
Choose the name of this type of sequence.

ATriangular numbersBCube numbersCSquare numbersDPrime numbers

4A pattern is made from tiles.
Pattern 1 uses $4$ tiles, Pattern 2 uses $7$, Pattern 3 uses $10$ and Pattern 4 uses $13$.
How many tiles are used in Pattern 10?

A31B28C30D34

5Here are the first four terms of a sequence.
$11,\ 3,\ -5,\ -13$
Work out the next two terms.

A-21, -29B-5, 3C21, 29D-22, -31

6The $n$th term of a sequence is $n^2 + 3$.
Work out the smallest integer $n$ for which the $n$th term is greater than $500$.

A25B23C24D22

7The 1st term of an arithmetic sequence is $43$ and the 4th term is $25$.
The same amount is added or subtracted each time.
Find the term-to-term rule.

Asubtract 7Bsubtract 18Cadd 6Dsubtract 6

8In this number chain the same two steps repeat: “$\times 3$ then $-5$”, then “$+5$”, alternating.
The chain so far is:
$5, \; 10, \; 15, \; 40, \; 45, \; \boxed{?}$
The next step is “$\times 3$ then $-5$”.
Work out the next number in the chain.

A135B130C50D125

9A list is made of $n$ consecutive whole numbers (for example $7, 8, 9, 10, 11$ is a list of $5$ of them).
Write an expression, in terms of $n$, for the range of a list of $n$ consecutive whole numbers.

An - 1BnC2n - 1Dn + 1

10In this sequence, each term after the second is the sum of the two terms before it.
The 1st, 3rd, 4th and 5th terms are
$2, \; \boxed{?}, \; 5, \; 8, \; 13$
Work out the missing 2nd term.

A7B5C3D2

11Each term of this Fibonacci-type sequence is the sum of the two terms before it.
$4,\ 3,\ 7,\ \boxed{\phantom{0}},\ 17$
Work out the missing term.

A24B11C17D10

12The first three terms of a sequence are
$a,\ b,\ ab,\ \ldots$
Each term after the first two is the product of the two terms before it.
Find the 6th term, in terms of $a$ and $b$.

A$a^5b^3$B$a^2b^4$C$a^3b^5$D$a^2b^3$

13The population of a town is modelled by $P_{n+1} = a\,P_n + 800$, where $P_n$ is the population at the start of year $n$.
At the start of year 1 the population is $25000$, and at the start of year 2 it is $30800$.
Use the model to work out the population at the start of year 4.

A56134B46112C45312D37760

A$8a+12b$B$5a+8b$C$13a+8b$D$8a+13b$

15The first three terms of a sequence are
$p,\ q,\ pq,\ \ldots$
Each term after the first two is the product of the two terms before it.
Find the 5th term, in terms of $p$ and $q$.

A$p^2q^3$B$p^2q^2$C$pq^2$D$p^3q^2$

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Sequences & Patterns · MCQ assessment

Version J

Tick one box (A, B, C or D) for each question. 15 questions, 1 mark each.Name: __________ Class: ______

Mark bar · shade a box for each question you got right

123456789101112131415

/ 15

1Here is a sequence.
$5,\ 20,\ 80,\ 320$
Write down the term-to-term rule for this sequence.

Amultiply by 5Bmultiply by 3Cadd 15Dmultiply by 4

2Here is a sequence with one term missing.
$7,\ 10,\ \boxed{\phantom{00}},\ 16,\ 19$
Work out the value of the missing term.

A14B13C10D16

3Here are the first four terms of a sequence.
$4,\ -3,\ -10,\ -17$
Work out the next two terms.

A-24, -31B24, 31C-10, -3D-25, -33

4In a Fibonacci-type sequence, each term is the sum of the two terms before it.
Here are the first four terms of such a sequence.
$2,\ 4,\ 6,\ 10$
Write down the next two terms.

A16, 26B11, 17C16, 42D20, 36

5Here are some consecutive terms of a well-known sequence.
$10,\ 15,\ 21,\ 28,\ 36$
Write down the next two terms.

A55, 45B81, 100C44, 52D45, 55

6In this number chain the same two steps repeat: “$\times 3$ then $-2$”, then “$+2$”, alternating.
The chain so far is:
$5, \; 13, \; 15, \; 43, \; 45, \; \boxed{?}$
The next step is “$\times 3$ then $-2$”.
Work out the next number in the chain.

A131B133C135D47

7Each term of this Fibonacci-type sequence is the sum of the two terms before it.
$4,\ 6,\ \boxed{\phantom{0}},\ 16,\ 26$
Work out the missing term.

A22B10C16D11

8Aisha says that $79$ is a triangular number.
Is Aisha correct? You must give a reason.

ANo, it is not a triangular numberBNo, but only because it is oddCYes, it is a triangular numberDIt cannot be decided without a calculator

9The $n$th term of a sequence is $n^2 + 5$.
Work out the smallest integer $n$ for which the $n$th term is greater than $500$.

A23B24C25D22

10A list is made of $n$ consecutive whole numbers (for example $6, 7, 8, 9, 10, 11, 12$ is a list of $7$ of them).
Write an expression, in terms of $n$, for the range of a list of $n$ consecutive whole numbers.

A2n - 1Bn + 1Cn - 1Dn

11In this sequence, each term after the second is the sum of the two terms before it.
The 1st, 3rd, 4th and 5th terms are
$3, \; \boxed{?}, \; 11, \; 19, \; 30$
Work out the missing 2nd term.

A3B11C8D14

A46840B45840C38200D57208

13The first three terms of a sequence are
$p,\ q,\ pq,\ \ldots$
Each term after the first two is the product of the two terms before it.
Find the 6th term, in terms of $p$ and $q$.

A$p^3q^5$B$p^2q^4$C$p^5q^3$D$p^2q^3$

14The first three terms of a Fibonacci-type sequence are $a$, $b$ and $a+b$.
Each term after the first two is the sum of the two terms before it.
The sequence begins
$a,\ b,\ a+b,\ a+2b,\ \ldots$
Find the 7th term, in terms of $a$ and $b$.

A$3a+5b$B$8a+5b$C$5a+8b$D$5a+7b$

15The population of a town is modelled by $P_{n+1} = a\,P_n + 800$, where $P_n$ is the population at the start of year $n$.
At the start of year 1 the population is $40000$, and at the start of year 2 it is $48800$.
Use the model to work out the population at the start of year 4.

A59360B87238C71232D72032

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