Question

If a, b, c are in A.P., then $2^{ax+1},2^{bx+1},2^{cx+1},x\ne 0$ are in-

• A. A.P.
• B. G.P. when x > 0
• C. G.P. if x < 0
• D. G.P. for all $x\ne 0$

Answer 1

The correct option is D G.P. for all $x\ne 0$

Given $a,b,c$ be in A.P, then
$2b=a+c$... (i)
$(2^{bx+1}{)}^2=(2^{2bx+2})=2^{ax+1}\times 2^{cx+1}$ [Using (i)]
Therefore, the given terms are in G.P.