CAT 2025 Slot 3 QA Q2 Progressions & Series

Question 2 of the Quantitative Ability (QA) section, CAT 2025 Slot 3, with CAT's official answer and a worked solution.

In an arithmetic progression, if the sum of fourth, seventh and tenth terms is 99, and the sum of the first fourteen terms is 497, then the sum of first five terms is

TITA: type in the answer. There are no options and no negative marking.

Answer: 65 Progressions & Series TITA

Solution

  1. \(T_4 + T_7 + T_{10} = 3T_7 = 99\), so \(T_7 = 33\).
  2. \(S_{14} = 7(T_1 + T_{14}) = 7(T_7 + T_8) = 497\), so \(T_7 + T_8 = 71\) and \(T_8 = 38\).
  3. Hence \(d = 5\) and \(T_1 = 33 - 6 \times 5 = 3\).
  4. \(S_5 = \frac{5}{2}(2 \times 3 + 4 \times 5) = 65\).

Shortcut. \(S_5 = 5 \times T_3 = 5 \times 13 = 65\).

Same concept in other years

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

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