Chapter 14 - Sequences, Series, and the Binomial Theorem - 14.2 Arithmetic Sequences and Series - 14.2 Exercise Set - Page 902: 37

$S_{50}=2550$

The first n term of an arithmetic sequence can be calculated as: $S_n=\frac{n}{2}(a_1+a_n)$ We have to find the sum of the even numbers from 2 to 100. $a_1=2$ $a_{n}=100$ There are 50 even numbers from 2 to 100, inclusive. Therefore we can substitute in the formula of the sum, and we get: $S_{50}=\frac{50}{2}(2+100))=25\times102=2550$