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What should come in place of the question mark (?) in the given series? 8, 24, 49, 85, 134, ?
181
191
198
180
198
Calculate the difference between consecutive terms; the pattern follows the sequence of squares of consecutive integers: 4 squared, 5 squared, 6 squared, 7 squared, and 8 squared.
Calculate the difference between consecutive terms; the pattern follows the sequence of squares of consecutive integers: 4 squared, 5 squared, 6 squared, 7 squared, and 8 squared.
Calculate first-level differences
24 - 8 = 16, 49 - 24 = 25, 85 - 49 = 36, 134 - 85 = 49.
Identify the pattern of differences
The differences are 16 (4 squared), 25 (5 squared), 36 (6 squared), and 49 (7 squared). The next difference must be 8 squared, which is 64.
Calculate the final term
Add the next difference to the last term: 134 + 64 = 198.
A: 181 is incorrect as it results from adding 47 instead of 64. B: 191 is incorrect as it results from adding 57 instead of 64. D: 180 is incorrect as it results from adding 46 instead of 64.
C is correct because the series follows a pattern of adding consecutive squares (4², 5², 6², 7², 8²) to each preceding term, where 134 + 64 equals 198.
When a series grows rapidly, always check the difference between terms; if the differences are not constant, check the square or cube of the integers.
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