Find the sum of all the even numbers from 12 through 58?

Answer 1

840

There are a several ways to approach this problem, the most staightforward being to to simply add all of them up.

Another is to let X be the sum of all of the even numbers from 12 through 58.

X=12+14+16+...+54+56+58

But X also can be expressed as follows:

X=58+56+54+...+16+14+12

If you add these two equations term by term, you'll notice that each term sums to 70 (12+58, 14+56, 16+54, etc.). You should also note that there are 24 70's when you add them up (i.e., there are 24 even numbers from 12 through 58. Adding the two equations above, you get:

2X=70+70+70+...+70+70+70=70*24

Dividing both side by two, you get your result: X=70*24/2 = 840.