Question

If$a,\frac{1}{b},c$ and $\frac{1}{p},q,\frac{1}{r}$form two arithmetic progression of the same common difference, then a, q, c are in A.P. if

• A. p, b, r are in A.P.
• B. are in A.P.
• C. p, b, r are in G.P.
• D. none of these

Answer 1

The correct option is B

are in A.P.

Since a, q and c are in A.P., so

$2q=a+c$

$\Rightarrow \frac{1}{p}+\frac{1}{r}=\frac{2}{b}$

$\Rightarrow \frac{1}{p},\frac{1}{b},\frac{1}{r}$ are in A.P