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📐 Mathematics  ·  Sequences and Series  ·  JEE

Between two numbers a and b, n geometric means are inserted. The product of all n means equals:

Answer: (ab) n/2.

  • A (ab)<sup>n/2</sup>
  • B (ab)<sup>n</sup>
  • C ab × n
  • D n√(ab)

Correct answer: A. (ab)<sup>n/2</sup>

Explanation: The n geometric means form a GP between a and b. Their product = (ab)<sup>n/2</sup>. This follows because the means pair up symmetrically.

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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