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Multiplication of Monomials

In an A.P, th...

Question

In an A.P, the sum of first $n$ terms is $4 n^{2} - 3 n$ . Its $n^{t h}$ term is $8 n - a$ . Find a.

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Solution

$a_{r} = s_{n} - S_{n - 1}$
$= 4 n^{2} - 3 n - [4 (n - 1)^{2} - 3 (n - 1)]$
$= 4 n^{2} - 3 n - [4 (n^{2} - 2 n + 1) - 3 n + 3]$
$= 4 n^{2} - 3 n - 4 n^{2} + 8 n - 4 + 3 n - 3$
$= 8 n - 7$

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