Question:
The sum of first q terms of an A.P. is $63 q-3 q^{2}$. If its pth term is $-60$, find the value of $p$. Also, find the 11 th term of this A.P.
Solution:
$S_{q}=63 q-3 q^{2}$
We know
$a_{q}=S_{q}-S_{q-1}$
$\therefore a_{q}=63 q-3 q^{2}-63(q-1)+3(q-1)^{2}$
$a_{q}=66-6 q$
Now, $a_{p}=-60$
$\Rightarrow 66-6 p=-60$
$\Rightarrow 126=6 p$
$\Rightarrow p=21$
$a_{11}=66-6 \times 11=0$
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