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📐 Mathematics  ·  Sequences and Series  ·  JEE

In a GP, if a₁ + a₂ + a₃ = 13 and a₁a₂a₃ = 27, find the common ratio.

Answer: 1/3 or 3.

  • A 1/3 or 3
  • B 2 or 1/2
  • C 1 or 1
  • D 3 or -3

Correct answer: A. 1/3 or 3

Explanation: Three numbers in GP: a/r, a, ar. Product: a³ = 27, a = 3. Sum: 3/r + 3 + 3r = 13. 3r² - 10r + 3 = 0. (3r-1)(r-3) = 0. r = 1/3 or 3.

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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