Identify the incorrect term in the numerical sequence provided below.

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

The correct answer is 124.

To find the incorrect term in the numerical sequence, let us analyze the differences between consecutive terms in the given sequence:

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

Step 1: Calculate the first differences between consecutive terms.

19 - 6 = 13

58 - 19 = 39

124 - 58 = 66

214 - 124 = 90

331 - 214 = 117

474 - 331 = 143

Step 2: Identify the pattern in the differences.

Looking at the differences: 13, 39, ..., ..., 117, 143

Notice that 13, 39, 117, and 143 are all multiples of 26 apart (or multiples of 13):

13 = 13 × 1

39 = 13 × 3

117 = 13 × 9

143 = 13 × 11

The second differences between these valid terms are constant (equal to 26):

39 - 13 = 26

143 - 117 = 26

Therefore, the sequence of first differences should increase by 26 at each step:

1st difference: 13

2nd difference: 13 + 26 = 39

3rd difference: 39 + 26 = 65

4th difference: 65 + 26 = 91

5th difference: 91 + 26 = 117

6th difference: 117 + 26 = 143

Step 3: Reconstruct the correct sequence using the valid differences.

1st term: 6

2nd term: 6 + 13 = 19

3rd term: 19 + 39 = 58

4th term (correct): 58 + 65 = 123

5th term: 123 + 91 = 214

6th term: 214 + 117 = 331

7th term: 331 + 143 = 474

Comparing the given sequence with the correct sequence, the 4th term given is 124 instead of 123.

Hence, 124 is the incorrect term in the sequence.