The sum of the first 8 terms of a GP is five times the sum of its first 4 terms. If r 1 is the common ratio, then what is the number of possible real values of r?

NDA 2025 Mathematics question

The sum of the first 8 terms of a GP is five times the sum of its first 4 terms. If is the common ratio, then what is the number of possible real values of ?

(A)One
(B)Two
(C)ThreeCorrect
(D)More than three

Answer: (C)

Solution

For , and . The condition gives , i.e. . So or . Real solutions:

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Question ID VK-030013