2024 CSAT, all questions
UPSC Prelims 2024 · CSAT
Question 46: Logical Reasoning and Mental Ability
What is the sum of the first 28 terms in the following sequence? 1, 1, 2, 1, 3, 2, 1, 4, 3, 2, 1, 5, 4, 3, 2, ···
a83
b84
c85
d86
AnswerUPSC’s answer is (b).
Group the terms: 1 | 1, 2 | 1, 3, 2 | 1, 4, 3, 2 and so on. Group k has k terms: a 1, then k down to 2. Its sum is 1 + (2 + … + k) = k(k + 1)/2, the triangular number. The first 28 terms are exactly groups 1 to 7, since 1 + 2 + … + 7 = 28 terms. Sum = 1 + 3 + 6 + 10 + 15 + 21 + 28 = 84.
Why each option is right or wrong
- (a) Wrong. 83 is one less than the group-wise total of 84.
- (b) Right. 1 + 3 + 6 + 10 + 15 + 21 + 28 = 84.
- (c) Wrong. 85 is one more than the group-wise total.
- (d) Wrong. 86 is two more than the group-wise total.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2024, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.