Question

If the 8th term of an H.P. is 1/2 and the 14th term is 1/3, then the 20th term is

• A. $\frac{1}{5}$
• B. $\frac{1}{4}$
• C. $-\frac{1}{2}$
• D. $\frac{1}{6}$

Answer 1

The correct option is B $\frac{1}{4}$

Let the H.P. be $\frac{1}{a},\frac{1}{a+d},\frac{1}{a+2d},.....a_8=\frac{1}{2}\Rightarrow \frac{1}{a+7d}=\frac{1}{2}\Rightarrow a+7d=2a_{14}=\frac{1}{3}\Rightarrow \frac{1}{a+13d}=\frac{1}{3}\Rightarrow a+13d=3\mathrm{Substracting}\mathrm{above}\mathrm{equations},6d=1\Rightarrow d=\frac{1}{6}\therefore a=\frac{5}{6}{a}_{20}=\frac{1}{a+19d}=\frac{1}{\frac{5}{6}+19\times \left(\frac{1}{6}\right)}=\frac{1}{4}$