Mathematics - Sequence & Series Question with Solution | TestHub

Suppose $d_1$ is the common difference of the A.P. $x_1,x_2,\dots .x_n$ then $$\begin{array}{rl}& \because x_8-x_3=5d_1=12\Rightarrow d_1=\frac{12}{5}=2.4\\ & \Rightarrow x_5=x_3+2d_1=8+2\times \frac{12}{5}=12.8\end{array}$$ Suppose $d_2$ is the common difference of the A.P $\frac{1}{h_1},\frac{1}{h_2},\dots .\cdot \frac{1}{h_n}$ then $$\begin{array}{rl}& 5d_2=\frac{1}{20}-\frac{1}{8}=\frac{-3}{40}\Rightarrow d_2=\frac{-3}{200}\\ & \because \frac{1}{h_{10}}=\frac{1}{h_7}+3d_2=\frac{1}{200}\Rightarrow h_{10}=200\\ & \Rightarrow x_5.h_{10}=12.8\times 200=2560\end{array}$$