Question

If $A_1,A_2$ be two arithmetic means between $\frac{1}{3}$ and $\frac{1}{24}$, then their values are

• A. $\frac{7}{72},\frac{5}{63}$
• B. $\frac{17}{72},\frac{5}{36}$
• C. $\frac{7}{36},\frac{5}{72}$
• D. $\frac{5}{72},\frac{17}{72}$

Answer 1

The correct option is B $\frac{17}{72},\frac{5}{36}$

Let the common difference $=d$

$\Rightarrow \frac{1}{3},A_1,A_2,\frac{1}{24}$

$A_1=\frac{1}{3}+d$

$A_2=\frac{1}{3}+2d$ $\therefore A_1=\frac{1}{3}+\left(\frac{-7}{72}\right)$

$\frac{1}{24}=\frac{1}{3}+3d$ $A_1=\frac{17}{72}$

$3d=\frac{1}{24}-\frac{1}{3}$ $A_2=\frac{1}{3}+2\left(\frac{-7}{72}\right)$

$\therefore d=\frac{-7}{72}$ $A_2=\frac{5}{36}$