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📐 Mathematics  ·  Sequences and Series  ·  JEE

An infinite GP has sum 15 and the sum of the squares of its terms is 45. Its first term is:

Answer: 5.

  • A 3
  • B 5
  • C 10
  • D 15/2

Correct answer: B. 5

Explanation: a/(1−r) = 15 and a²/(1−r²) = 45. Dividing, a/(1+r) = 3. With a = 15(1−r) this gives r = 2/3 and a = 5.

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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