VT · Sequences & Patterns

Non-calculator

In each set, one thing changes and everything else stays the same. Work them out in order and look for the pattern — the last line tells you what to notice.

①Same start, only the common difference changeschanging: the common difference

Write the NEXT term. Each sequence starts $3, \ldots$

$3,\ 5,\ 7,\ \ldots$

$3,\ 7,\ 11,\ \ldots$

$3,\ 8,\ 13,\ \ldots$

The start is always $3$; a bigger step gives a bigger next term.

②Same rule (add 4), only the start changeschanging: the first term

Write the NEXT term. Each sequence adds $4$ each time.

$2,\ 6,\ 10,\ \ldots$

$5,\ 9,\ 13,\ \ldots$

$1,\ 5,\ 9,\ \ldots$

The rule is always "add $4$"; only the starting number changes.

③Fibonacci-type: add the previous twochanging: the two starting terms

Write the NEXT term (add the previous two).

$1,\ 1,\ 2,\ 3,\ \ldots$

$2,\ 3,\ 5,\ 8,\ \ldots$

$4,\ 5,\ 9,\ 14,\ \ldots$

Each term is the sum of the two before it; the start decides everything.

Answers · Sequences & Patterns

Variation practice

① Same start, only the common difference changes

$3,\ 5,\ 7,\ \ldots$: 9$3,\ 7,\ 11,\ \ldots$: 15$3,\ 8,\ 13,\ \ldots$: 18

② Same rule (add 4), only the start changes

$2,\ 6,\ 10,\ \ldots$: 14$5,\ 9,\ 13,\ \ldots$: 17$1,\ 5,\ 9,\ \ldots$: 13

③ Fibonacci-type: add the previous two

$1,\ 1,\ 2,\ 3,\ \ldots$: 5$2,\ 3,\ 5,\ 8,\ \ldots$: 13$4,\ 5,\ 9,\ 14,\ \ldots$: 23