# Thread: What is the purpose of this question?

1. ## What is the purpose of this question?

Obtain the general term, $a_n$, of the sequence denoted by $S_n=3n^2-2n$, where $S_n$ is the sum of the first $n$ terms

To my understanding, is the question asking if you're given an equation $S_n$, which is the general equation of the sum of the first $n$ terms of an arithmetic sequence (is that correct), and you have to find the general term of the arithmetic sequence that $S_n$ represents, right?

2. Yes, that's exactly what the problem asks. Notice that since $S_n= a_1+ a_2+ \cdot\cdot\cdot$ $+ a_{n-1}+ a_n$ and $S_{n-1}= a_1+ a_2+$ $\cdot\cdot\cdot+ a_{n-1}$, $a_n$ is just $S_n- S_{n-1}$.