$\text{ If }{\mathrm{x}}_1,{\mathrm{x}}_2,\dots {\mathrm{x}}_{\mathrm{n}}\text{ and }\frac{1}{{\mathrm{h}}_1},\frac{1}{{\mathrm{h}}_2},.\frac{1}{{\mathrm{h}}_{\mathrm{n}}}\text{ are two A.P's such that }{\mathrm{x}}_3={\mathrm{h}}_2=8\text{ and }{\mathrm{x}}_8={\mathrm{h}}_7=20$ $\text{ then }{\mathrm{x}}_5{\mathrm{h}}_{10}\text{ is }$

${\mathrm{d}}_1\text{ is common difference of A.P of }{\mathrm{x}}_1,{\mathrm{x}}_2\dots {\mathrm{x}}_{\mathrm{n}}\text{ then }$

$\begin{array}{r}{\mathrm{x}}_8-{\mathrm{x}}_3=5{\mathrm{d}}_1=12\Rightarrow {\mathrm{d}}_1=2.4 \Rightarrow {\mathrm{x}}_5={\mathrm{x}}_3+2{\mathrm{d}}_1=8+2.\left(\frac{12}{5}\right)=12.8\\ \text{ Suppose }{\mathrm{d}}_2\text{ is the common difference of an A.P }\frac{1}{{\mathrm{h}}_1},\frac{1}{{\mathrm{h}}_2},\cdot \cdot \frac{1}{{\mathrm{h}}_{\mathrm{n}}}\end{array}$

$\begin{array}{l}\frac{1}{h_7}-\frac{1}{h_2}=5{\mathrm{d}}_2=\frac{1}{20}-\frac{1}{8}=-3/40\\ {\mathrm{d}}_2=\frac{-3}{200}\\ \because \frac{1}{{\mathrm{h}}_{10}}=\frac{1}{{\mathrm{h}}_7}+3{\mathrm{d}}_2=\frac{1}{20}-\frac{9}{200}=\frac{1}{200}\Rightarrow {\mathrm{h}}_{10}=200\\ \therefore {\mathrm{x}}_5\cdot {\mathrm{h}}_{10}=12.8\times 200=2560\end{array}$