Question

Find the second, fifth, and ninth terms of a sequence where the first term is 65 and the common difference is -7.

Answer 1

There are multiple ways to do this.

The easiest is to just continuously subtract 7 from 65 the numbers of times needed.

But most math teachers will have you use the equation ar^n-1 where a= the first term (65), r=ratio (-7), and n=the term you need (second, fifth, and ninth). 

So to solve you just plug your values in as so
AR^n-1

(65)(-7)^2-1(65)(-7)^5-1
(65)(-7)^9-1