Question

If $\frac{1}{p},\frac{1}{q},\frac{1}{r}$ are in A.P where $p+q+r\ne 0$ then $\frac{q+r}{p},\frac{r+p}{q},\frac{p+q}{r}$ are also in

• A. A.P
• B. G.P
• C. H.P
• D. A.G.P

Answer 1

The correct option is A A.P

Given:$\frac{1}{p},\frac{1}{q},\frac{1}{r}$ are in A.P

$\Rightarrow \frac{p+q+r}{p},\frac{p+q+r}{q},\frac{p+q+r}{r}$ are in A.P

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

$\Rightarrow \frac{q+r}{p},\frac{p+r}{q},\frac{p+q}{r}$ are in A.P