Sum of numbers from 1 to n
= half x n x (n + 1)

In this case, sum of numbers from 1 to 25
= half x 25 x 26
= 325

Last digit is 5.

There is a way to predict the last digit without calculating everything.

Observe that in the first 10 numbers, from 1 to 10,

1 + 9 = 10
2 + 8 = 10
3 + 7 = 10
4 + 6 = 10
5 is alone, so in the first 10 numbers, the last digit of their sum is 5.

In the first 20 numbers, the "5" in 5 and the "5" in 15 add to 20 with a last digit of 0, so the last digit of their sum is 0.

Then 21 + 22 + 23 + 24 has a last digit of 0, while 25 has a last digit of 5.

So the last digit of the sum 1 to 25 must be 5.

Rainbow method :

1 + 25 = 26
2 + 24 = 26
3 + 23 = 26
.
.
.
10 + 16 = 26
11 + 15 = 26
12 + 14 = 26

Each pair adds up to 26. There are 12 pairs. Number 13 is unpaired.

12 x 26 → the ones digit of the product is 2 (you don't actually have to multiply out, since we know the product of 6 and 2 (in the ones place) is 12)

add this 2 to the 3 in 13

2 + 3 = 5