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What should come in place of the question mark (?) in the given series?
85 94 108 127 151?
170
175
180
185
180
Calculate the difference between adjacent terms to find the pattern. Here, the differences increase continuously by prime numbers starting from 9, or simply add consecutive prime numbers starting from 9 to the base sequence.
Calculate the difference between adjacent terms to find the pattern. Here, the differences increase continuously by prime numbers starting from 9, or simply add consecutive prime numbers starting from 9 to the base sequence.
Calculate the first-level differences
Find the difference between consecutive terms in the series: 94 - 85 = 9, 108 - 94 = 14, 127 - 108 = 19, 151 - 127 = 24.
Analyze the difference pattern
Look at the sequence of differences: 9, 14, 19, 24. Find the second-level difference: 14 - 9 = 5, 19 - 14 = 5, 24 - 19 = 5. The differences are increasing by a constant value of +5 each time.
Find the next difference and term
The next difference in the sequence will be 24 + 5 = 29. Adding this difference to the last term (151) gives: 151 + 29 = 180.
A: 170 is incorrect as it assumes a difference of 19 instead of 29. B: 175 is incorrect as it assumes a difference of 24 instead of 29. D: 185 is incorrect as it assumes a difference of 34 instead of 29.
C is correct because the series follows a double-difference pattern where the term-to-term differences increase by 5 each step (+9, +14, +19, +24, +29), yielding 151 + 29 = 180.
When faced with an increasing number series where terms grow slowly, always compute the first-level differences immediately; if no clear pattern emerges, compute the second-level differences.
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