Mathematics - Sequence & Series Question with Solution | TestHub

Let $d_1$ be the common difference of the A.P. $x_1,x_2,\dots$, then $x_8-x_3=5{ d}_1=12\Rightarrow$

$\Rightarrow x_5=x_3+2{ d}_1=8+2\times \frac{12}{5}=12.8$

Let $d_2$ be the common difference of the other sequence then

$5{ d}_2=\frac{1}{20}-\frac{1}{8}=\frac{-3}{40}\Rightarrow d_2$

$\Rightarrow \frac{1}{{ h}_{10}}=\frac{1}{{ h}_7}+3{ d}_2=\frac{1}{200}\Rightarrow h_{10}=200$

$\Rightarrow x_5·h_{10}=12.8\times 200=2560$