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Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked
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What should come in place of the question mark (?) in the series: 12, 25, 48, 81, 124, ?
175
177
182
168
177
Find the differences between consecutive terms (13, 23, 33, 43), notice a constant second difference of 10, and add the next difference (53) to the last term.
Find the differences between consecutive terms (13, 23, 33, 43), notice a constant second difference of 10, and add the next difference (53) to the last term.
Find First Differences
Calculate the difference between each consecutive term: 25 minus 12 is 13, 48 minus 25 is 23, 81 minus 48 is 33, and 124 minus 81 is 43.
Identify Second Difference Pattern
Examine the sequence of differences (13, 23, 33, 43). They form an arithmetic progression increasing by a constant value of 10 at each step.
Calculate the Missing Term
The next difference in the sequence will be 43 plus 10, which equals 53. Adding this to the last term gives 124 plus 53 equals 177.
A: 175 is incorrect because it results from an incorrect difference addition; C: 182 is incorrect as it overshoots the correct arithmetic growth; D: 168 is incorrect because it underestimates the required next difference.
B is correct because the series follows a double difference pattern where consecutive differences increase by 10, resulting in 124 + 53 = 177.
When first-level differences do not show a uniform pattern, immediately check the second-level differences to uncover hidden arithmetic progressions.
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