Question

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

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

Answer 1

The correct option is D

$10$

The explanation for the correct answer.

Solve for the fifth term of the HP $2,2\frac{1}{2},3\frac{1}{3}$

Finding reciprocals.

$2,2\frac{1}{2},3\frac{1}{3}=2,\frac{5}{2},\frac{10}{3}$

The reciprocal of H.P. terms in A.P.

So$\frac{1}{2},\frac{2}{5}$, and $\frac{3}{10}$ are in AP.

Here, The first term $a=\frac{1}{2}$

The common difference, $d=-\frac{1}{10}$

${\mathit{a}}_{\mathbf{n}}\mathbf{=}\mathit{a}\mathbf{+}\mathbf{(}\mathit{n}\mathbf{-}\mathbf{1}\mathbf{)}\mathit{d}$

$5$th term of AP $=a+4d$

$=\frac{1}{2}-\frac{4}{10}=\frac{1}{10}$

So,$5$th term HP $=10$

Hence, option(D) is the correct answer.