1

A growing pattern uses counters.
Pattern 1 uses $6$ counters, Pattern 2 uses $11$ and Pattern 3 uses $16$.
How many more counters are needed to go from one pattern to the next? [2]

2

Here is a sequence with one term missing.
$36,\ 31,\ \boxed{\phantom{00}},\ 21,\ 16$
Work out the value of the missing term. [2]

3

A pattern is made from matchsticks.
Pattern 1 uses $6$ matchsticks, Pattern 2 uses $10$, Pattern 3 uses $14$ and Pattern 4 uses $18$.
How many matchsticks are used in Pattern 8? [3]

4

Each term of this Fibonacci-type sequence is the sum of the two terms before it.
$1,\ 5,\ \boxed{\phantom{0}},\ 11,\ 17$
Work out the missing term. [2]

5

In this number chain the same two steps repeat: “$\times 2$ then $-1$”, then “$+1$”, alternating. The chain so far is:
$4, \; 7, \; 8, \; 15, \; 16, \; \boxed{?}$
The next step is “$\times 2$ then $-1$”. Work out the next number in the chain. [3]

6

In this sequence, each term after the second is the sum of the two terms before it. The 1st, 3rd, 4th and 5th terms are
$2, \; \boxed{?}, \; 9, \; 16, \; 25$
Work out the missing 2nd term. [3]

7

The 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. [3]

8

The 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. [3]