Question

If $P,Q$ be two arithmetic means between $\frac{1}{3}$ and $\frac{1}{24}$, then their value are

• A. $\frac{7}{72},\frac{5}{36}$
• 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 $\frac{17}{72},\frac{5}{36}$

P and Q are the arithmetic means between $\frac{1}{3}$ and $\frac{1}{24}$

So the resulting sequence formed an AP

$\frac{1}{3},P,Q,\frac{1}{24}$ are in AP

$\Rightarrow a_4=a+(4-1)d$

$\Rightarrow \frac{1}{24}=\frac{1}{3}+(4-1)d$

$\Rightarrow \frac{-7}{24}=3d$

$\Rightarrow d=\frac{-7}{72}$

$\therefore P=a+d=\frac{1}{3}+\frac{-7}{72}$

=$\frac{24-7}{72}$

=$\frac{17}{72}$

and $Q=a+2d=\frac{1}{3}+\frac{-14}{72}$

=$\frac{24-14}{72}$

=$\frac{5}{36}$