Question

The second, fourth and the sixteenth term of an increasing arithmetic progression are consecutive terms of a geometric progression, If the first term of the A.P is −3, find the common ratio of the G.P.

Answer 1

a+d, a+3d,a+15d
−3 +15d  = −3 + 3d
−3 + 3d        −3+d
9+
 9−45d −3d + 15d² = 9 − 18d + 9d²
  −30d = −6d²
        d = 5
 −3 + 75 =  72
  −3  +15    12
       r=6