Question

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

Answer 1

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

$\Rightarrow$ The sequence is $3^a$, $3^{a+d}$, $3^{a+2d}$ $\equiv$ $3^a$, $3^a$ $\times$ $3^d$, $3^a$ $\times$ ${\left(3^d\right)}^2$

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