Question

If a, b, c are in A.P. then $3^a$, $3^b$, $3^c$ are in ___.

• A. A.P.
• B. G.P.
• C. H.P.
• D. None of these

Answer 1

The correct option is B

G.P.

Let the A.P. be a, a+d, a+2d.

$\Rightarrow$ The sequence is $3^a$, $3^{a+d}$, $3^{a+2d}$.

$\equiv$ $3^a$, $3^a$$\times$ $3^d$, $3^a$ $\times$ ${\left(3^d\right)}^2$

Common ratio
$=\frac{3^a\times 3^d}{3^a}$

$=\frac{3^a\times {\left(3^d\right)}^2}{3^d\times 3^a}$

$=3^d$

$\Rightarrow$ It is a G.P. with common ratio $3^d$ and first term $3^a$.