Question

If $1,a,b$ and $4$ are in harmonic progression, then the value of $a+b$ is equal to

• A. $\frac{5}{4}$
• B. $\frac{10}{3}$
• C. $\frac{3}{10}$
• D. $\frac{4}{5}$

Answer 1

Answer: (B)

$1,\frac{1}{a},\frac{1}{b},\frac{1}{4}$ are in A.P.
Its common difference $D=\frac{\frac{1}{4}-1}{3}=\frac{-1}{4}$
$\Rightarrow \frac{1}{a}=1+\left(-\frac{1}{4}\right)=\frac{3}{4}\Rightarrow a=\frac{4}{3}$
$\frac{1}{b}=1+2\left(-\frac{1}{4}\right)=\frac{1}{2}\Rightarrow b=2$
$\Rightarrow a+b=\frac{4}{3}+2=\frac{10}{3}$