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What should come in place of the question mark (?) in the given series? 17 22 37 62 97 ?
137
140
142
148
142
Calculate the successive differences between consecutive terms. If the first-level difference increases by a constant value (+5 each time), it is a two-tier arithmetic progression.
Calculate the successive differences between consecutive terms. If the first-level difference increases by a constant value (+5 each time), it is a two-tier arithmetic progression.
Step 1: Find the First Difference
Calculate the difference between consecutive terms: 22 - 17 = 5, 37 - 22 = 15, 62 - 37 = 25, 97 - 62 = 35.
Step 2: Identify the Second Difference Pattern
The differences are 5, 15, 25, 35. These form an arithmetic progression increasing by a constant value of +10 at each step.
Step 3: Determine the Next Difference
Following the +10 increment pattern, the next difference after 35 is 35 + 10 = 45.
Step 4: Calculate the Missing Term
Add the final difference to the last given term: 97 + 45 = 142, which matches Option C.
A: 137 is incorrect because it adds 40 instead of the required 45 difference. B: 140 is incorrect due to an arithmetic calculation error. D: 148 is incorrect as it results from adding an incorrect difference of 51.
C is correct because the series follows a two-tier arithmetic progression where the differences between consecutive terms increase by 10 (+5, +15, +25, +35, +45), leading to 97 + 45 = 142.
When first-level differences do not yield a constant, always calculate the second-level difference (difference of differences) to easily crack quadratic or two-tier series patterns.
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