Discussion
Which will replace the question mark in the given series?
27, 64, 125, 216, ?
Answer: D
The terms are the cubes of 3, 4, 5 and 6: \(27 = 3^3\), \(64 = 4^3\), \(125 = 5^3\) and \(216 = 6^3\). The next term is the cube of 7.
\[ 7^3 = 343 \]
The values 340, 341 and 342 are close to 343 but are not cubes. The answer is 343, option D.
As a check, the gaps between terms are 37, 61 and 91, which increase by 24 and 30, so the next gap is 36 more than 91, that is 127, and 216 + 127 = 343, which agrees with the cube of 7.
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