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CAT 2024 Slot 3 · Quant · Progressions · medium

An arithmetic progression has first term 5 and common difference 3.

Single correct option

An arithmetic progression has first term 5 and common difference 3. If the sum of the first n terms is 670, find n.
  1. A. 18
  2. B. 19
  3. C. 20
  4. D. 22
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Answer: (C) 20

Sₙ = n/2 × [2a + (n−1)d] = n/2 × [10 + 3(n−1)] = n/2 × (3n+7) = 670. So 3n² + 7n − 1340 = 0. Solving, n = 20 (the other root is negative and rejected). Check: S₂₀ = 20/2 × (10+57) = 10×67 = 670. ✓
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Original question written in the CAT 2024 Slot 3 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake