Find out the missing term of the number series given below.

25, ?, 256, 476, 745, 1050

The correct option is 100.

To find the missing term of the number series, let us analyze the differences between consecutive terms. Let the missing term in the series be represented by x. The series is:
25, x, 256, 476, 745, 1050

If we substitute the correct answer, x = 100, we get the following sequence:
25, 100, 256, 476, 745, 1050

Let us calculate the first differences between consecutive terms of this sequence:

$100-25=75$

$256-100=156$

$476-256=220$

$745-476=269$

$1050-745=305$

Now, let us examine the differences of these first differences (the second differences) to check for a logical pattern:

$156-75=81=9^2$

$220-156=64=8^2$

The second differences are consecutive perfect squares in decreasing order: 81, 64, 49, 36 (or 9², 8², 7², 6²). Since this pattern is perfectly consistent, the missing term must indeed be 100.