If a, b, c are in A.P., then 2ax+1,2bx+1,2cx+1,x∈R are in

a, b, c are in A.P. ⇒ 2ax,2bx,2cx are in G.P.⇒2ax+1,2bx+1,2cx+1are in G.P.

a, b, c are in A.P. ⇒ 2ax,2bx,2cx are in G.P.⇒2ax+1,2bx+1,2cx+1are in G.P.

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If $a, b, c$ are in A.P., then $2^{a x + 1}, 2^{b x + 1}, 2^{c x + 1}, x \in R$ are in

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A.P.

G.P. and when x > 0

G.P. only when x < 0

G.P. for all x

answer is D.

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a, b, c are in A.P. $\Rightarrow 2^{a x}, 2^{b x}, 2^{c x}$ are in G.P.

$\Rightarrow 2^{a x + 1}, 2^{b x + 1}, 2^{c x + 1}$ are in G.P.

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