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📐 Mathematics  ·  Sequences and Series  ·  JEE

The sum of an arithmetic-geometric series a + (a+d)r + (a+2d)r² + ... to infinity (|r|<1) is:

Answer: a/(1-r) + dr/(1-r)².

  • A a/(1-r) + dr/(1-r)²
  • B a/(1-r)
  • C dr/(1-r)
  • D a + dr/(1-r)²

Correct answer: A. a/(1-r) + dr/(1-r)²

Explanation: Let S = a + (a+d)r + (a+2d)r² +… Multiply by r: rS = ar + (a+d)r² +… Subtract: S(1−r) = a/(1−r) + dr/(1−r). So S = a/(1−r) + dr/(1−r)².

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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