Sequences and Series: AP-GP link MCQ

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AP-GP linkHardQuestion 210038

Question

If a, b, c are in AP and a², b², c² are in GP, and a < b < c with a + b + c = 3/2, then b equals:

A
1/2
Correct
B
1
C
3/4
D
1/3

Correct answer

1/2

Explanation

Let a = b−d, c = b+d. Sum = 3b = 3/2 → b = 1/2. For GP: b⁴ = a²c² → b² = ±ac. With a = 1/2−d, c = 1/2+d: (1/4) = (1/4−d²) → d = 0 or the constraint from sign. b = 1/2.

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