📐 Mathematics · Sequences and Series · JEE

If x, y, z are in GP and a^x = b^y = c^z, then a, b, c are in:

Answer: HP.

A AP
B GP
C HP
D No relation

Correct answer: C. HP

Explanation: Let a^x = b^y = c^z = k. Then a = k^1/x, b = k^1/y, c = k^1/z. Since x,y,z in GP: y² = xz, so 1/y is between 1/x and 1/z in harmonic proportion. Thus a,b,c are in HP.

Bar heights for AP 2, 5, 8, 11 with the common difference d=3 marked between consecutive terms.

Concept context

Arithmetic progressions, geometric progressions, and sums

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If x, y, z are in GP and ax = by = cz, then a, b, c are in:

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