The sum of first q terms of an A.P. is 63q − 3q2.

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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