The first term of an AP is 12 and that of a GP is 6. The common difference and the common ratio are equal, so as are the sum of the fist 3 terms. Find the possible values of the common difference?

Answer 1

12 + 12+d + 12+2d = 6(1+r+r^2)
But, d=r, so
36+3d = 6(1+d+d^2)
6d^2+3d-30 = 0
2d^2 + d - 10 = 0
(2d+5)(d-2) = 0
So, d=2 or -5/2

The two sequences are thus

12,14,16
6,12,24
with S3=42

or,

12,9.5,7
6,-15,75/2
with S3=28.5