What is the difference of the sum of numbers 1 through 25 and numbers 26 through 50?

Question

What is the difference of the sum of numbers 1 through 25 and numbers 26 through 50?

Answer 1

Sum 1-25 = (25)(25 + 1)/2 = (25)(26)/2 = (25)(13) = 325

Sum 26-50 = (50 - 25)(50 + 26)/2 = (25)(76)/2 = 25(38) = 950

950 - 325 = 625

Answer 2

You can change the second list into the first list by removing 25 from each number.

So the second sum becomes (25+1) + (25+2) + (25+3)...

You can rearrange the order of the elements:

(25 + 25 + ... + 25) + 1 + 2 + 3 + ... + 25

= (25*25) + (1 + 2 + 3 +...+25)

the right bracket is the same as the first sum (1 to 25), the difference is adding 25 to itself 25 times.  25*25 = 625

Answer 3

The difference in the sum is 625

Each number from 26 through 50 is 25 more than the corresponding number from 1 through 25, and there are a total of 25 numbers in each series

so 25 * 25 = 625

sum from 1-25 = 25(26)/2 = 325

sum from 26-50 = 25(76)/2 = 950