In a G.P., if the product of the first three terms is 27 and the set of all possible values for the sum of its first three terms is R - (a, b), then a2 + b2 is equal to .
90
Let the first three terms be Ar, A, Ar (r 0).
Product = A3 = 27 A = 3
Sum S = 3 (r + 1 + 1r )
r + 1r 2 for r > 0 and r + 1r -2 for r < 0
1 + r + 1r (- , -1] [3, )
S (- , -3] [9, ) = R - (-3, 9)
a = -3, b = 9
a2 + b2 = 9 + 81 = 90
Answer: 90
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