The product of three consecutive terms of a G.P. is 512. If 4 is added to each of the first and the second of these terms, the three terms now form an A.P. Then the sum of the original three terms of the given G.P. is?

The correct option is D 28
Let terms be a/r, a, ar → G.P
Product = (a/r) * a * ar = a³ = 512
a = 8
If 4 is added to the first and second terms, then the terms are:
a/r + 4, a + 4, ar
Since they are in A.P.,
2(a + 4) = a/r + 4 + ar
2(8 + 4) = 8/r + 4 + 8r
24 = 8/r + 4 + 8r
20 = 8/r + 8r
20r = 8 + 8r²
8r² - 20r + 8 = 0
2r² - 5r + 2 = 0
(2r - 1)(r - 2) = 0
r = 1/2 or r = 2
If r = 2, terms are 4, 8, 16
Sum = 4 + 8 + 16 = 28
If r = 1/2, terms are 16, 8, 4
Sum = 16 + 8 + 4 = 28