Finding the nth term of a linear sequence

Sometimes, rather than finding the next number in a linear sequence, you want to work out the {41}^{st} number, or the {110}^{th} number.

Writing out {41} or {110} numbers takes too much time, so you can use a general rule.

To find the value of any term in a sequence, use the n^{th} term rule.


What is the {n}^{th} term of this sequence?

Linear sequence diagram




So the n^{th} term is 5 \times n or 5n

For example, to find the {10}^{th} term, work out 5 \times 10 = 50. To find the {7}^{th} term, work out 5 \times 7 = 35.

So the {41}^{st} term is 5 \times 41 = 205 and the {110}^{th} term is 5 \times 110 = 550


What are the n^{th} term and the {10}^{th} term of this sequence:

{2},~{4},~{6}, ... ?

{n}^{th} term = 2n

{10}^{th} term = 20.

To work this out, n = 10, so 2n = 2 \times 10 = 20