Two methods:

Method 1:

The sum is twice the sum 1 + 2 + ... + 150, so there
are 150 terms.

Here is how to do it without using any formulas:

Let S represent the sum.  

 S =   2 +   4 +   6 +   8 + ... + 294 + 296 + 298 + 300

Under that write the sum of the 150 terms in descending order:

 S =   2 +   4 +   6 +   8 + ... + 294 + 296 + 298 + 300
 S = 300 + 298 + 296 + 294 + ... +   8 +   6 +   4 +   2 

Add them term by term:
 S =   2 +   4 +   6 +   8 + ... + 294 + 296 + 298 + 300
 S = 300 + 298 + 296 + 294 + ... +   8 +   6 +   4 +   2 
 -------------------------------------------------------
2S = 302 + 302 + 302 + 302 + ... + 302 + 302 + 302 + 302

Therefore since there are 150 terms, there are 150 302's on the right,
so 

2S = 150*302

2S = 45300

 S = 22650

Method 2:

Using formulas for an arithmetic series:

, , 














Edwin