Question

If the $7th$ term of a $HP$ is $\frac{1}{10}$ and the $12th$ term is $\frac{1}{25}$ , then the $20th$ term is

• A. $\frac{1}{41}$
• B. $\frac{1}{45}$
• C. $\frac{1}{49}$
• D. $\frac{1}{37}$

Answer 1

Answer: (C)

Since, 7 th term of HP is $\frac{1}{10}$ and 12 th term is $\frac{1}{25}$.
Its corresponding terms of $AP$ is 10 and 25 .
$\therefore T_7=a+(n-1)d=10$
$\Rightarrow a+(7-1)d=10$
$\Rightarrow a+6d=10\dots (i)$
and $T_{12}=a+(12-1)d=25$
$\Rightarrow a+11d=25\dots (ii)$
On solving Eqs. (i) and (ii), we get
$a=-8,d=3$
$\therefore T_{20}=-8+(20-1)3$
$=-8+57$
$=49$
Then, 20 th term of $HP$ is $\frac{1}{49}$.