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 in the given number series, let us analyze the differences between consecutive terms:

$256-100=156$

$476-256=220$

$745-476=269$

$1050-745=305$

Now, let us examine the differences between these consecutive differences (the second-order difference):

$220-156=64$

$269-220=49$

$305-269=36$

We can see that the second-order differences are decreasing perfect squares:

$64=8^2$

$49=7^2$

$36=6^2$

Following this pattern backwards, the previous second-order difference must be:

$9^2=81$

Thus, the first difference between the first term (25) and the missing term (?) must satisfy:

$156-81=75$

Finally, we add this difference of 75 to the first term (25) to find the missing term:

$25+75=100$

Therefore, the missing term is 100.