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

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

NTA AbhyasNTA Abhyas 2020Sequences and Series

Solution:

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