Question

The first term of an A.P. is 2 and the last term is 50. The sum of all these terms is 442. Find the common difference.

Answer 1

$$\begin{gathered} \mathrm{Given}: \\ a=2,l=50,S_n=442 \\ \mathrm{Now},S_n=442 \\ \Rightarrow \frac{n}{2}\left[a+l\right]=442 \\ \Rightarrow \frac{n}{2}\left[2+50\right]=442 \\ \Rightarrow n=17 \\ \therefore a_{17}=50 \\ \Rightarrow a+(17-1)\times d=50 \\ \Rightarrow 2+16d=50 \\ \Rightarrow d=3 \end{gathered}$$