Fully worked, step-by-step solutions to GCSE Generating sequences questions. See exactly how to solve problems on term-to-term rule, generating terms, continuing a sequence, position-to-term rule.
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: for the first term, for the second, and so on.
Substitute
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
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.
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