If a,b,c are in A.P., then 2^{ax +1} , ^{2bx +1}_, 2^{cx +1} , x ≠ 0 are in

(1) A.P

(2) G.P only when x > 0

(3) G.P if x < 0

(4) G.P for all x ≠ 0

Solution:

Since a, b, c are in AP

2b = a+c

(2^{bx +1})² = (2^{2bx +2})

= 2^{(a+c)x +2}

= 2^ax+1 × 2^cx+1

=> 2^{ax +1} , ^{2bx +1}_, 2^{cx +1} are in GP.

Hence option (4) is the answer.