Question

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

Answer 1

$S_q=63q-3q^2$

$T_p=-60$

$S_1=a_1=63-3=60$

$S_2=a_1+a_2=63\left(2\right)-\left(34\right)=114$

$a_1+a_1+d=114$

$d=114-2\left(60\right)=-6$

$T_p=a+(p-1)d$

$\Rightarrow -60=60+(p+1)(-6)$

$\Rightarrow \frac{-120}{-6}=(p-1)$

$\Rightarrow 20=p-1$

$\Rightarrow p=21$

$T_{11}=a+10d=60+10(-6)=0$.