How do you decide if a term is in a sequence?

If you have the rule of a sequence for the nth term, you can set this equal to your number, and then find the value of n. If n is an integer (whole number) then the number is in the sequence. If not, then it isn't.

For example, if our rule is 2n+1, and we want to know if the number 15 is in the sequence we set:

15=2n+1

So 2n=16

And n=8

8 is a whole number, so 15 is in the sequence.