# Finding a of n from Sn partial sum

1. Sep 28, 2013

### freshman2013

1. The problem statement, all variables and given/known data

suppose that the partial sum of the series (sigma)n=1,infinity an is given by the partial sum Sn = (-2n+9)/(-6n+15). Find an expression for an when n>1

2. Relevant equations

Sn= (-2n+9)/(6n+15

3. The attempt at a solution
So I attempted to subtract S(n-1) from S(n) to get each term for an and got the following terms
a2=8/9
3=-8/3
4=8/9
5=8/45
6=8/105
7=8/189
8=8/297
How am I supposed to come up with a generalized expression from these terms, or am I wrong from the first step of doing S(n)-S(n-1) to get those terms for an? The only pattern I can recognize is that after a4, the difference of the denominators increase by 24 from one term to the next.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

Last edited: Sep 28, 2013
2. Sep 28, 2013

### Dick

$S_{n}-S_{n-1}=a_n$. So take your expression for $S_n$ and subtract the same expression with n-1 substituted for n. Putting numbers in isn't the way to do it.