# How many terms of the arithmetic sequence 2,4,6,8, ... add up to 60,762?

##### 1 Answer

Jul 14, 2015

Let

So

#### Explanation:

A standard property of sums of arithmetic sequences is:

Intuitively, the terms of an arithmetic sequence are evenly spaced, so the average value is the same as the average of the two outermost terms.

For our sequence, we have

and we want to solve:

Now

So

So

Check: