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📐 Mathematics  ·  Sequences and Series  ·  JEE

If a, b, c are in HP, then b =

Answer: 2ac/(a+c).

  • A 2ac/(a+c)
  • B (a+c)/2
  • C √(ac)
  • D (a+c)/ac

Correct answer: A. 2ac/(a+c)

Explanation: HP means 1/a, 1/b, 1/c are in AP. So 2/b = 1/a + 1/c = (a+c)/ac. Solving: b = 2ac/(a+c), the harmonic mean of a and c.

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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