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Which of the following numbers will replace the question mark (?) in the given series? 30, 31, 36, 45, 62, ?
88
87
85
90
87
Observe the differences between consecutive terms; they form a sequence of powers of 1 (or specific squares) adjusted by a pattern, specifically looking at the differences: 1, 5, 9, 17, 25.
Observe the differences between consecutive terms; they form a sequence of powers of 1 (or specific squares) adjusted by a pattern, specifically looking at the differences: 1, 5, 9, 17, 25.
Calculate the differences between consecutive terms
31 - 30 = 1; 36 - 31 = 5; 45 - 36 = 9; 62 - 45 = 17.
Analyze the pattern of the differences
The differences are 1, 5, 9, 17. Looking at the secondary differences: 5 - 1 = 4; 9 - 5 = 4; 17 - 9 = 8. This indicates the primary difference increases by 4, 4, 8... wait, let us re-examine: 1 to 5 is +4, 5 to 9 is +4, 9 to 17 is +8. The next gap is +8, so 17 + 8 = 25. Thus, 62 + 25 = 87.
A: 88 is incorrect as it results from adding 26 instead of 25 to 62. C: 85 is incorrect as it results from adding 23 to 62. D: 90 is incorrect as it results from adding 28 to 62.
B is correct because the sequence of differences (1, 5, 9, 17, 25) follows a pattern where the increments increase in groups (4, 4, 8, 8), making the final term 62 + 25 = 87.
When single-layer differences do not show an obvious pattern, always calculate the difference of the differences (second-layer difference) to uncover hidden logic.
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