CAT 2024 Slot 1 QA Q14 Progressions & Series

Question 14 of the Quantitative Ability (QA) section, CAT 2024 Slot 1, with CAT's official answer and a worked solution.

Suppose \(x_1, x_2, x_3, \ldots, x_{100}\) are in arithmetic progression such that \(x_5=-4\) and \(2 x_6+2 x_9=x_{11}+x_{13}\). Then, \(x_{100}\) equals
  1. A
    204
  2. B
    -194
  3. C
    -196
  4. D
    206

Answer: (B) -194 Progressions & Series MCQ

Solution

  1. Let \(x_n = x_1 + (n-1)d\).
  2. \(2x_6 + 2x_9 = 4x_1 + 26d\) and \(x_{11} + x_{13} = 2x_1 + 22d\). Equating: \(2x_1 = -4d \Rightarrow x_1 = -2d\).
  3. \(x_5 = x_1 + 4d = 2d = -4 \Rightarrow d = -2,\ x_1 = 4\).
  4. \(x_{100} = 4 + 99 \times (-2) = -194\).

Same concept in other years

See every question on AP problems: write terms as a + (n − 1)d and solve.

More Progressions & Series questions from CAT

All 38 Progressions & Series questions asked since 2017.