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Which number is wrong in the series 2, 6, 15, 31, 56, 93?3169356

Question

Which number is wrong in the series 2, 6, 15, 31, 56, 93?3169356

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Solution

The series seems to be increasing in a pattern. Let's try to figure out the pattern:

  1. The difference between 6 and 2 is 4.
  2. The difference between 15 and 6 is 9.
  3. The difference between 31 and 15 is 16.
  4. The difference between 56 and 31 is 25.
  5. The difference between 93 and 56 is 37.

If we look at these differences, we can see that they are not consistent. However, if we look closer, we can see that they are all perfect squares (4 is 2^2, 9 is 3^2, 16 is 4^2, 25 is 5^2).

So, the pattern seems to be that each number in the series is the previous number plus the square of a consecutive integer.

If we apply this pattern, the difference between 56 and 31 should be 36 (which is 6^2), not 25. Therefore, the number 56 in the series is wrong. It should be 67 (31 + 6^2).

This problem has been solved

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