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Series

If the sum of...

Question

If the sum of $n$ terms of a series is given by $S_{n} = n^{2} - n,$ then its $10^{t h}$ term is

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Solution

Let $T_{n}$ be the $n^{t h}$ term of series
$T_{n} = S_{n} - S_{n - 1} = n^{2} - n - [(n - 1)^{2} - (n - 1)] = n^{2} - n - [n^{2} - 3 n + 2] = 2 n - 2$

Hence,
$T_{10} = 2 \times 10 - 2 = 18$

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