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What should come in place of the question mark (?) in the following series? 11, 17, 29, 47, 71, ?
101
99
100
102
101
Identify the difference between consecutive terms; here, the differences themselves form a sequence of multiples of 6 (6, 12, 18, 24, 30).
Identify the difference between consecutive terms; here, the differences themselves form a sequence of multiples of 6 (6, 12, 18, 24, 30).
Analyze consecutive differences
Calculate the difference between each pair: 17-11=6; 29-17=12; 47-29=18; 71-47=24.
Identify the pattern in differences
The differences (6, 12, 18, 24) increase by 6 each time. Following this logic, the next difference must be 24 + 6 = 30.
Calculate the final term
Add the next difference to the last known term: 71 + 30 = 101.
B: 99 is incorrect as it results from adding 28 instead of 30. C: 100 is incorrect as it follows no valid progression. D: 102 is incorrect as it results from adding 31 instead of 30.
A is correct because the series follows a pattern of adding successive multiples of 6 (6, 12, 18, 24, 30) to the preceding number, resulting in 71 + 30 = 101.
When a series grows slowly, always check the first-order difference first. If that doesn't reveal a clear pattern, check the difference of the differences (second-order difference).
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