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CAT 2016 Slot 2 · Quant · Progressions · medium

The sum of the first n terms of an arithmetic progression is 3n² + 5n. What is its 12th term?

Single correct option

The sum of the first n terms of an arithmetic progression is 3n² + 5n. What is its 12th term?
  1. A. 68
  2. B. 72
  3. C. 74
  4. D. 80
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Answer: (C) 74

Tₙ = Sₙ − Sₙ₋₁ = [3n² + 5n] − [3(n − 1)² + 5(n − 1)] = 6n + 2.

T₁₂ = 6 × 12 + 2 = 74.

Check: T₁ = S₁ = 8 and the common difference = 6, so T₁₂ = 8 + 11 × 6 = 74. ✓

Tip: if Sₙ = An² + Bn, then d = 2A and T₁ = A + B.
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Original question written in the CAT 2016 Slot 2 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake