If 3rd term of an H.P. is 7 and 7^th term of H.P. is 3 then 10^th term is

$$\begin{gathered} \frac{1}{\mathrm{a}+2\mathrm{d}}=7 \Rightarrow \mathrm{a}+2\mathrm{d}=\frac{1}{7} -\left(1\right) \\ \frac{1}{\mathrm{a}+6\mathrm{d}}=3 \Rightarrow \mathrm{a}+6\mathrm{d}=\frac{1}{3} -\left(2\right) \\ \left(1\right)-\left(2\right) \Rightarrow -4\mathrm{d}=\frac{1}{7}-\frac{1}{3} \Rightarrow 4\mathrm{d}=\frac{4}{21} \\ \Rightarrow \mathrm{d}=\frac{1}{21} \\ \mathrm{a}=\frac{1}{7}-2\mathrm{d}=\frac{1}{7}-\frac{2}{21}=\frac{3-2}{21}=\frac{1}{21} \\ {a}_{10}=\frac{1}{\mathrm{a}+9\mathrm{d}}=\frac{1}{{\displaystyle \frac{1}{21}}+{\displaystyle \frac{9}{21}}}=\frac{21}{10} \end{gathered}$$