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Question 210035
JEE Mathematics · Hard

Sequences and Series: Integer sum MCQ

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Integer sumHardQuestion 210035

Question

How many terms of the AP 1, 4, 7, ... are needed for the sum to first exceed 500?
  1. A
    18
    Correct
  2. B
    19
  3. C
    17
  4. D
    20

Correct answer

18

Explanation

Sₙ = n(2 + (n−1)3)/2 = n(3n−1)/2 > 500. So 3n²−n > 1000. Testing n=18: 3(324)−18 = 972−18 = 954 > 1000? No: 954/2 = 477. n=19: 3(361)−19 = 1083−19=1064; 1064/2 = 532 > 500. So n = 19.

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