Directions: Identify the incorrect number in the series given below:

100, 107, 121, 142, 172, 205, 247

The incorrect number in the series is 172.

To find the incorrect number, let us analyze the pattern of differences between consecutive terms in the given series:

$107-100=7$

$121-107=14$

$142-121=21$

Notice that the differences between consecutive terms are consecutive multiples of 7 (7, 14, 21, 28, 35, 42).

Following this pattern, the next difference after 21 should be $28$:

$142+28=170$

However, the given term in the series is 172 instead of 170.

Let us verify the remaining terms of the series using 170:

$170+35=205$

$205+42=247$

Since both remaining terms match the given series when using 170, the incorrect number in the series is 172.