JAMB 1997 · UME · Q19

$S_n$ is the sum of the first $n$ terms of a series given by $S_n = n^2 - 1$ . Find the $n$ th term.

Worked solution (try it first)

The $n$ th term is the sum of $n$ terms minus the sum of $n - 1$ terms: $T_n = S_n - S_{n - 1}$ .
So $T_n = (n^2 - 1) - \big((n - 1)^2 - 1\big)$
$= n^2 - (n - 1)^2$ .
Expand: $n^2 - (n^2 - 2n + 1) = 2n - 1$ , option D.