Generating sequences Worked Solutions — GCSE Maths

Write down the first term

The sequence starts at $5$.

Apply the term-to-term rule 'add $4$'

A term-to-term rule tells you how to get from one term to the NEXT one: add $4$ to the term before.

Work out the second term

$5$ add $4$ is $9$, so the second term is $9$.

Write down the first term

The sequence starts at $2$.

Find the second term

Add $7$ to the first term.

Find the third term

Add $7$ again — this time to the SECOND term, not to the first.

Find the last term you are given

The next term is built from the term you already have at the end.

Apply the rule to that term

The rule says add $4$ to the previous term.

Work out the next term

The next term is $19$.

Write down the position-to-term rule

Here n stands for the POSITION of the term: $n = 1$ for the first term, $n = 2$ for the second, and so on.

Substitute $n = 1$

The first term means the term in position $1$.

Work out the value

The first term is $5$.

Write down the position-to-term rule

n is the position number of the term you want.

Substitute $n = 5$

For the 5th term you put 5 in place of n.

Work out the value

Multiply before you add, so the $5th$ term is $17$.