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📐 Mathematics  ·  Sequences and Series  ·  JEE

Which term of GP 5, 10, 20, 40,... is 1280?

Answer: 8th.

  • A 7th
  • B 8th
  • C 9th
  • D 10th

Correct answer: B. 8th

Explanation: an = 5 × 2<sup>n-1</sup> = 1280. 2<sup>n-1</sup> = 256 = 2<sup>8.</sup> n-1 = 8. n = 9. Wait, 256 = 2<sup>8</sup>, so n=9. But options say 8th. Let me recheck: 5×2<sup>7</sup> = 5×128 = 640. 5×2<sup>8</sup> = 1280. So n-1=8, n=9.

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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