Find nth term given the equation of a series.

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I want to find the $n$th term when the sum of the series is given.

In general, this is done by $a_n = s_n - s_{n-1}$. But I don't get it why I am not getting the same answer with $s_{n+1} - s_n$.

Shouldn't they both give $a_n$ (the general term)?