Discussion
Select the number from among the given options that can replace the question mark (?) in the following series.
6, 7, 15, 24, 88, ?, 329
Answer: A
The missing number is 113. The series adds a square and a cube alternately: \[ 6 + 1 = 7 \] \[ 7 + 2^{3} = 15 \] \[ 15 + 3^{2} = 24 \] \[ 24 + 4^{3} = 88 \] \[ 88 + 5^{2} = 113 \] \[ 113 + 6^{3} = 329 \] The last step reaches the given 329 exactly, which confirms the pattern. The other options 114, 115 and 116 would leave a gap that is not 216, so the final cube would not fit. Checking the last step shows that 113 + 216 = 329, which agrees with the number given in the series.
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