Question

The fifth term of the H.P., $2,2\frac{1}{2},3\frac{1}{3},...................$ will be

• A. $5\frac{1}{5}$
• B. $3\frac{1}{5}$
• C. $\frac{1}{10}$
• D. $10$

Answer 1

Answer: (D)

Series $2,2\frac{1}{2},3\frac{1}{3},........$ are in H.P.
$\Rightarrow \frac{1}{2},\frac{2}{5},\frac{3}{10},..........$ will be in A.P.
Now, first term $a=\frac{1}{2}$
and common difference $d=-\frac{1}{10}$
So, $5^{th}$ term of the A.P. $=\frac{1}{2}+(5-1)\left(-\frac{1}{10}\right)=\frac{1}{10}$.
Hence, $5^{th}$ term in H.P. is 10 .