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📐 Mathematics  ·  Sequences and Series  ·  JEE

If three numbers are in HP, their reciprocals are in AP. If HP is 1/2, 1/3, 1/4, the AP is:

Answer: 2, 3, 4.

  • A 2, 3, 4
  • B 4, 3, 2
  • C 1/4, 1/3, 1/2
  • D 2, 4, 6

Correct answer: A. 2, 3, 4

Explanation: HP definition: reciprocals form AP. Reciprocals of 1/2, 1/3, 1/4 are 2, 3, 4. Check: common difference = 1 throughout. AP is 2, 3, 4.

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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