Question

The sum of first q terms of an A.P. is 63q − 3q². If its pth term is −60, find the value of p. Also, find the 11th term of this A.P.

Answer 1

$$\begin{gathered} S_q=63q-3q^2 \\ \mathrm{We}\mathrm{know} \\ {a}_q=S_q-S_{q-1} \\ \therefore a_q=63q-3q^2-63\left(q-1\right)+3{\left(q-1\right)}^2 \\ {a}_q=66-6q \\ \mathrm{Now},a_p=-60 \\ \Rightarrow 66-6p=-60 \\ \Rightarrow 126=6p \\ \Rightarrow p=21 \\ {a}_{11}=66-6\times 11=0 \end{gathered}$$