Question

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

• A. $p,b,r$ are in A.P.
• B. $\frac{1}{p},\frac{1}{b},\frac{1}{r}$ are in A.P.
• C. $p,b,r$ are in G.P.
• D. none of these

Answer 1

Answer: (A)

$p,b,r$ 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.