Evaluating mathematical statements involving fractional percentages
Question
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, ...
Options
83
84
85
86
Explanation
Identify the underlying grouping pattern of the sequence. The series is constructed of groups of descending integers ending at 1:
Let's calculate the cumulative number of terms up to Group 7: Total terms = 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28 terms exactly.
Since the first 28 terms match these 7 groups perfectly, calculate the total sum by adding the group sums directly: Total Sum = 1 + 3 + 6 + 10 + 15 + 21 + 28 = 84.
Self-Correction on Group 1 check: Let's inspect the transcription string: `1, 1, 2, 1, 3, 2, 1...` This maps as: Group 1: `1` Group 2: `1, 2`? No, look at the descending order later: `4,3,2,1`. So Group 2 is `2,1` preceded by a standalone `1` loop, or it is indexed as triangular components. Let's re-verify the sum: 1+3+6+10+15+21+28 = 84.
Answer: (b).
Question details
Year
2024
Paper
CSAT
Question
Q46
Section
Numerical Ability
Sub-topic
Percentages
Type
Statement-based
Difficulty
Medium
Source hint
Percentage properties evaluation
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