In the following number series, only one number is incorrect. Identify the wrong number:

6, 19, 58, 124, 214, 331, 474

Question

In the following number series, only one number is incorrect. Identify the wrong number:

6, 19, 58, 124, 214, 331, 474

Accepted Answer

**Solution:**

1. Observe the series: 6, 19, 58, 124, 214, 331, 474

2. Check the pattern by examining the differences between consecutive terms:
   - 19 - 6 = 13
   - 58 - 19 = 39
   - 124 - 58 = 66
   - 214 - 124 = 90
   - 331 - 214 = 117
   - 474 - 331 = 143

3. The differences are: 13, 39, 66, 90, 117, 143

4. Now, check the pattern in the differences:
   - Differences between these differences:
     - 39 - 13 = 26
     - 66 - 39 = 27
     - 90 - 66 = 24
     - 117 - 90 = 27
     - 143 - 117 = 26

5. The second-level differences are not consistent, indicating the original series may have an error.

6. Try to find a pattern in the differences. If we consider the differences as multiples of 13:
   - 13 (13 × 1)
   - 39 (13 × 3)
   - 65 (13 × 5) instead of 66
   - 91 (13 × 7) instead of 90
   - 117 (13 × 9)
   - 143 (13 × 11)

7. The difference 66 should be 65 and 90 should be 91 to maintain the pattern of increasing odd multiples of 13.

8. Since 124 - 58 = 66 (incorrect), if it were 65, then the next term would be:
   - 58 + 65 = 123 (instead of 124)

9. Therefore, the wrong number in the series is **124**.

**Answer:** 124

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