How do I find the nth term of a sequence?

For any sequence where there is a common difference (it increases or decreases with the same amount, n, each time) you can find the nth term using the formula: dn+(a-d)

"a" is the value of the first term in the sequence

"d" is the common difference between the terms

To find the nth term you find the values of "a" and "d" and stick them in the formula, dn+(a-d)

For example: Find the nth term of this sequence: 3,7,11,15

The first term is 3, so a=3

The common difference is 4 (as it increases by 4 each time), so d=4

By using the formula we get, 4n+(3-4), which is equal to 4n-1

We can check this works by subbing in values of n into the formula and you will see that it is correct. 

Laura M. GCSE Maths tutor

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