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Thread: What is the purpose of this question?

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

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

    To my understanding, is the question asking if you're given an equation $\displaystyle S_n$, which is the general equation of the sum of the first $\displaystyle n$ terms of an arithmetic sequence (is that correct), and you have to find the general term of the arithmetic sequence that $\displaystyle S_n$ represents, right?
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  2. #2
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    Yes, that's exactly what the problem asks. Notice that since $\displaystyle S_n= a_1+ a_2+ \cdot\cdot\cdot$$\displaystyle + a_{n-1}+ a_n$ and $\displaystyle S_{n-1}= a_1+ a_2+$$\displaystyle \cdot\cdot\cdot+ a_{n-1}$, $\displaystyle a_n$ is just $\displaystyle S_n- S_{n-1}$.
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