Question

If $a,b,c$ are in A.P. and $k$ is any non zero number, then $k^a,k^b,k^c$ are in......

• A. H.P.
• B. G.P.
• C. A.G.P.
• D. A.P.

Answer 1

The correct option is B (G.P).

Given $a,b,c$ are in A.P, then their common difference for any consecutive terms is same.
So, $b-a=c-a$
Let $k^a,k^b,k^c$ are in G.P then their common ratio is same.
So, $\frac{k^b}{k^a}=\frac{k^c}{k^b}$
$\Rightarrow k^{b-a}=k^{c-b}$ [Since, $\frac{x^m}{x^n}=x^{m-n}$]
$\Rightarrow b-a=c-b$ which is true.
Hence, $k^a,k^b,k^c$ are in G.P