Question

The 7th term of an H.P. is $\frac{1}{10}$ and 12th term is $\frac{1}{25}$, find the 20th term.

• A. $\frac{1}{62}$
• B. $\frac{1}{64}$
• C. $\frac{1}{49}$
• D. $\frac{1}{36}$

Answer 1

The correct option is C $\frac{1}{49}$

7th term of an H.P. is $\frac{1}{10}$ and 12th term is $\frac{1}{25}$

$\Rightarrow$ 7th term of A.P. is $10$ and 12th term is $25$

Let $a$ be the first term and $d$ be the common difference

i.e $a+6d=10$ and $a+11d=25$

Solving above equations gives $a=-8$ and $d=3$

20th term of A.P. is $a+19d=49$

$\therefore$ 20th term of H.P. is $\frac{1}{49}$

Hence, option C.