Question

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

• A. $\frac{10}{21}$
• B. $\frac{21}{10}$
• C. $\frac{10}{7}$
• D. $\frac{3}{7}$

Answer 1

The correct option is B $\frac{21}{10}$

Given , $\frac{1}{a+2d}=7,\frac{1}{a+6d}=3$

$\Rightarrow a+2d=\frac{1}{7}\&a+6d=\frac{1}{3}\Rightarrow 4d=\frac{1}{3}-\frac{1}{7}=\frac{4}{21}\Rightarrow d=\frac{1}{7}\Rightarrow a=\frac{1}{7}-\frac{2}{21}=\frac{1}{21}\Rightarrow a+9d=\frac{1}{21}+\frac{9}{21}=\frac{10}{21}\therefore \frac{1}{a+9d}=\frac{21}{10}$

$\Rightarrow {10}^{th}$ term of $HP$ is $\frac{21}{10}$