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📐 Mathematics  ·  Sequences and Series  ·  JEE

If the sum of first n terms is 3n² + 5n, is it AP? Find the common difference.

Answer: Yes, d = 6.

  • A Yes, d = 6
  • B No, it is not AP
  • C Yes, d = 3
  • D Yes, d = 5

Correct answer: A. Yes, d = 6

Explanation: Tₙ = Sₙ − Sₙ₋₁ = (3n²+5n) − (3(n−1)²+5(n−1)) = 3(2n−1)+5 = 6n+2. Linear in n → AP. d = T₂−T₁ = 14−8 = 6.

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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