The sum of first $q$ terms of an A.P is $63 q - 3 q^{2}$ . If its $p^{t h}$ term is $- 60$ , find the value of $p$ . Also, find the $11$ th term of this A.P

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Solution

$G i v e n q t e r m s = 63 q - 3 q 2$
$S 1 = 63 * 1 - 3 * 1 * 1$
$= 60 = a 1 s u m o f f i r s t 1 t e r m i s f i r s t t e r m$
$S 2 = 63 * 2 - 3 * 2 * 2$
$= 114$
$S 2 - S 1 = 114 - 60$
$= 54 = a 2$ Sum of first two terms - sum of first term is 2 nd term.
So , $d = 54 - 60 = - 6$
Now,
$a p = - 60$
$= a + (p - 1) d = - 60$
$= 60 + (p - 1) - 6 = - 60$
$= p - 1 = - 60 - 60 / - 6$
$= p = 21$
Now,
$a 11 = a + 10 d$
$= 60 + 10 * - 6$
$= 60 + - 60$
$= 0$

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The sum of first q terms of an AP is $(63 q - 3 q^{2})$ . If its pth term is - 60, find the value of p. Also, find the 11th term of its AP.

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