The GATE Grind

GATE 2025 XH2 (English) – Question 21

Reasoning and Comprehension · Quantitative reasoning · 2 marks · Multiple choice

Given a series 5, 8, 11, 14, …

If the $n^{th}$ term of the given series is 320, then $n$ (where, $n \ge 1$) is

  1. 104
  2. 105
  3. 106
  4. 107

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Correct answer: (C) 106

Explanation

The series is an arithmetic progression with first term 5 and common difference 3, so the $n^{th}$ term is $5 + 3(n - 1) = 3n + 2$. Setting $3n + 2 = 320$ gives $n = 106$.