Find a if $S_{n}$ = $5 n - n^{2}$

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Solution

Given that sum of the firest n terms of an AP is $5 n - n^{2}$
$S n = 5 n - n^{2}$
First term, $a_{1} = S_{1} = 5 (1) - (1)^{2} = 5 - 1 = 4$
Sum of first two terms = $S_{2} = 5 (2) - (2)^{2} = 10 - 4 = 6.$
Second term, $a - 2 = S_{2} - S_{1} = 6 - 4 = 2$
$d = a_{2} - a_{1} = 2 - 4 = - 2 a_{n} = a + (n - 1) d$
=4+(n-1)(-2)
=4-2n+2
=6-2n
$∴ n^{t h}$ term of an A.P=6 -2n.

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