If frac{1}{4}, a, b, frac{1}{19} form a H.P., | vedclass

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(A) Given that $\frac{1}{4}, a, b, \frac{1}{19}$ are in $H.P.$Therefore,their reciprocals $4, \frac{1}{a}, \frac{1}{b}, 19$ are in $A.P.$Let the $A.P.

Vedclass · Accepted Answer

$\frac{1}{9}, \frac{1}{14}$

Vedclass · Answer

(A) Given that $\frac{1}{4}, a, b, \frac{1}{19}$ are in $H.P.$Therefore,their reciprocals $4, \frac{1}{a}, \frac{1}{b}, 19$ are in $A.P.$Let the $A.P.$ be $4, 4+d, 4+2d, 4+3d$.Here,$4+3d = 19 \implies 3d = 15 \implies d = 5$.Thus,the terms are $4, 4+5, 4+10, 19$,which are $4, 9, 14, 19$.Comparing the terms,$\frac{1}{a} = 9 \implies a = \frac{1}{9}$ and $\frac{1}{b} = 14 \implies b = \frac{1}{14}$.

If $\frac{1}{4}, a, b, \frac{1}{19}$ form a $H.P.$,then the values of $a$ and $b$ are respectively:

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