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Q46·CSAT · Prelims 2024

Evaluating mathematical statements involving fractional percentages

NumericalPercentagesStatement-basedMedium

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

a

83

b

84

c

85

Answer
d

86

Explanation

Identify the underlying grouping pattern of the sequence. The series is constructed of groups of descending integers ending at 1:

Group 1: `1` (1 term, sum = 1)
Group 2: `2, 1` (2 terms, sum = 3)
Group 3: `3, 2, 1` (3 terms, sum = 6)
Group 4: `4, 3, 2, 1` (4 terms, sum = 10)
Group 5: `5, 4, 3, 2, 1` (5 terms, sum = 15)
Group 6: `6, 5, 4, 3, 2, 1` (6 terms, sum = 21)
Group 7: `7, 6, 5, 4, 3, 2, 1` (7 terms, sum = 28)

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.

For block-structured sequences, convert the required term index (N=28) into the sum of block sizes to find exactly where the sequence cuts off.

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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