Determine the incorrect term from the following numerical series.

21, 29, 45, 73, 125, 225, 421

The correct option is 21.

Let's analyze the pattern by taking the difference between consecutive terms in the series.

If we work backwards from the last term of the series:

421 - 225 = 196

${14}^2=196$

225 - 125 = 100

${10}^2=100$

125 - 73 = 52

Notice the pattern of differences when considering squared numbers with a decreasing difference of 4 in their bases:

${14}^2=196$

${10}^2=100$

$6^2=36$

$2^2=4$

${(-2)}^2=4$

${(-6)}^2=36$

Let's test this pattern forward starting from 29:

29 + (-2)² = 29 + 4 = 33 (Instead of 29, if the first term was 25: 25 + (-2)² = 29)

29 + 2² = 29 + 4 = 33 (or 25 + 4 = 29)

29 + 6² = 29 + 36 = 65... Wait, let's examine another consistent pattern:

Look at the differences between adjacent terms:

421 - 225 = 196 = 14²

225 - 125 = 100 = 10²

125 - 73 = 52 = 6² + 16

73 - 45 = 28 = 2² + 24

45 - 29 = 16 = 4²

29 - 21 = 8

Let's check powers of 2 plus a constant or double differences:

Differences: 8, 16, 28, 52, 100, 196

Second differences: 8, 12, 24, 48, 96

Notice that from 12 onwards, each second difference doubles:

12 × 2 = 24

24 × 2 = 48

48 × 2 = 96

To keep the doubling pattern consistent throughout (6, 12, 24, 48, 96):

The second difference preceding 12 should be 6.

If the second difference is 6, the first difference preceding 16 would be 16 - 6 = 10.

Then the first term should be 29 - 10 = 19 instead of 21.

Therefore, the term 21 is incorrect in the given series.