Question

The sum of first n terms of an A.P. whose first term is 8 and the common difference is 20 is equal to the sum of first 2n terms of another A.P. whose first term is $-30$ and common difference is 8 . Find n.

Answer 1

According to the question, we have
$$\begin{gathered} \frac{n}{2}\left[2\left(8\right)+\left(n-1\right)20\right]=\frac{{\displaystyle 2n}}{{\displaystyle 2}}\left[2\left(-30\right)+\left(2n-1\right)8\right] \\ \Rightarrow \left[16+20n-20\right]=2\left[-60+16n-8\right] \\ \Rightarrow 20n-4=-136+32n \\ \Rightarrow 12n=132 \\ \Rightarrow n=11 \end{gathered}$$