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 25, ?, 256, 476, 745, 1050, we can analyze the pattern of differences between consecutive terms.

Let us assume the missing term is 100, which gives the series:
25, 100, 256, 476, 745, 1050

Now, let's calculate the first differences between consecutive terms:
100 - 25 = 75
256 - 100 = 156
476 - 256 = 220
745 - 476 = 269
1050 - 745 = 305

This gives the first set of differences as:
75, 156, 220, 269, 305

Next, let's look at the differences of these differences (the second differences):
156 - 75 = 81
220 - 156 = 64
269 - 220 = 49
305 - 269 = 36

We can clearly see that the second differences form a sequence of decreasing perfect squares:
$81=9^2$
$64=8^2$
$49=7^2$
$36=6^2$

Working backwards to find the missing term (let's call it x):
The difference between the first two terms is:
$x-25=75$
Which gives:
$x=25+75=100$

The pattern is perfectly consistent, confirming that the missing term is 100.