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📐 Mathematics  ·  Sequences and Series  ·  JEE

If a, b, c are in GP and p, q, r are in AP, then a<sup>p</sup> × b<sup>q</sup> × c<sup>r</sup> =

Answer: b p+q+r.

  • A b<sup>p+q+r</sup>
  • B abc
  • C b<sup>p+r</sup> × b<sup>q</sup>
  • D abc = b<sup>p+q+r</sup>

Correct answer: A. b<sup>p+q+r</sup>

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

Each bar grows by the common difference d=3a1=2a2=5a3=8a4=11d=3

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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