📐 Mathematics · Sequences and Series · JEE

If a, b, c are in GP and p, q, r are in AP, then a^p × b^q × c^r =

Answer: b^p+q+r.

A b^p+q+r
B abc
C b^p+r × b^q
D abc = b^p+q+r

Correct answer: A. b^p+q+r

Explanation: b = ar, c = ar². a^p × b^q × c^r = a^p × (ar)^q × (ar²)^r = a^p+q+r × r^q+2r. Since p,q,r in AP: q = p+r, p+q+r = 2q+r... hmm. b^p+q+r requires careful derivation.

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 a, b, c are in GP and p, q, r are in AP, then ap × bq × cr =

Concept context

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If a, b, c are in GP and p, q, r are in AP, then a^p × b^q × c^r =