CAT 2022 Slot 2 QA Q19 Progressions & Series

Question 19 of the Quantitative Ability (QA) section, CAT 2022 Slot 2, with CAT's official answer and a worked solution.

Consider the arithmetic progression \(3,7,11, \ldots\) and let \(A_n\) denote the sum of the first \(n\) terms of this progression. Then the value of \(\frac{1}{25} \sum_{n=1}^{25} A_n\) is
  1. A
    404
  2. B
    442
  3. C
    455
  4. D
    415

Answer: (C) 455 Progressions & Series MCQ

Solution

  1. \(A_n=\frac n2[6+4(n-1)]=2n^2+n\).
  2. \(\sum_{1}^{25}A_n=2\cdot\frac{25\cdot26\cdot51}{6}+\frac{25\cdot26}{2}=11050+325=11375\).
  3. Divide by 25: 455.

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