Question

Find the sum of n terms of the A.P. whose kth terms is 5k + 1.

Answer 1

$$\begin{gathered} \mathrm{Given}: \\ {a}_k=5k+1 \\ \mathrm{For}k=1,a_1=5\times 1+1=6 \\ \mathrm{For}k=2,a_2=5\times 2+1=11 \\ \mathrm{For}k=n,a_n=5n+1 \\ \therefore S_n=\frac{n}{2}\left[a+a_n\right] \\ \Rightarrow S_n=\frac{n}{2}\left[6+5n+1\right]=\frac{n}{2}\left(5n+7\right) \end{gathered}$$