Question

The first and last terms of an A.P. are 1 and 11. If the sum of its terms is 36, then the number of terms will be
(a) 5
(b) 6
(c) 7
(d) 8

Answer 1

(b) 6

$$\begin{gathered} a=1,a_n=11,S_n=36 \\ \because a_n=11 \\ \Rightarrow a+\left(n-1\right)d=11 \\ \Rightarrow 1+\left(n-1\right)d=11 \\ \Rightarrow \left(n-1\right)d=10.....\left(1\right) \\ \mathrm{Also},S_n=36 \\ \Rightarrow \frac{n}{2}\left\{2a+\left(n-1\right)d\right\}=36 \\ \Rightarrow n\left\{2+10\right\}=72\left(\mathrm{Using}\left(1\right)\right) \\ \Rightarrow n=6 \end{gathered}$$