Question

If the ${\text{7}}^{\text{th}}$ term of an H.P. is $8$ and $8^{\text{th}}$ term is $7$, then its ${15}^{\text{th}}$ term is :

• A. $16$
• B. $14$
• C. $\frac{27}{14}$
• D. $\frac{56}{15}$

Answer 1

The correct option is D $\frac{56}{15}$

A sequence of numbers is called a harmonic progression if the reciprocal of the terms are in AP.

$7^{th}$ term of an A.P$=\frac{1}{8}$

$8^{th}$ term of an A.P$=\frac{1}{7}$

$\Rightarrow a+6d=\frac{1}{8}$

$\Rightarrow a+7d=\frac{1}{7}$

$\Rightarrow a+7d-a-6d=\frac{1}{7}-\frac{1}{8}$

$\Rightarrow d=\frac{8-7}{56}=\frac{1}{56}$

Now,$a=\frac{1}{7}-7d=\frac{1}{7}-7\times \frac{1}{56}=\frac{1}{7}-\frac{1}{8}=\frac{8-7}{56}=\frac{1}{56}$

$\therefore a=\frac{1}{56},d=\frac{1}{56}$

${15}^{th}$ term of A.P$=a+14d=\frac{1}{56}+14\times \frac{1}{56}=\frac{1+14}{56}=\frac{15}{56}$

${15}^{th}$ term of H.P$=\frac{56}{15}$