What will replace the question mark (?) in the following series?2, 12, 36, 80, 150, 252, ?.
Question
What will replace the question mark (?) in the following series?2, 12, 36, 80, 150, 252, ?.
Solution
The given series is: 2, 12, 36, 80, 150, 252, ?
This appears to be a series of numbers where each number is the result of a certain mathematical operation on its position in the series.
Let's try to find the pattern:
2 = 1^3 + 1 12 = 2^3 + 22 36 = 3^3 + 33 80 = 4^3 + 44 150 = 5^3 + 55 252 = 6^3 + 6*6
So, the pattern seems to be n^3 + n*n, where n is the position of the number in the series.
Therefore, the next number in the series should be 7^3 + 7*7 = 343 + 49 = 392.
So, the number that will replace the question mark (?) in the series is 392.
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