Solve them by the method of elimination. In an $A . P, S_{n} = 5 n^{2} + 11 n$ , find $T_{n}$ .

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Solution

$S_{n} = 5 n^{2} + 11 n$
$S_{n - 1} = 5 (n - 1)^{2} + 11 (n - 1)$
$T_{n} = S_{n} - S_{n - 1}$
$= 5 n^{2} + 11 n - 5 (n - 1)^{2} - 11 (n - 1)$
$= 5 (n^{2} - (n - 1)^{2}) + 11 (n - n + 1)$
$= 5 [(n - n + 1) (n + n - 1)] + 11$
$= 5 (2 n - 1) + 11$
$= 10 n - 5 + 11$
$= 10 n + 6$

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