Chapter 11 - Sequences; Induction; the Binomial Theorem - Section 11.2 Arithmetic Sequences - 11.2 Assess Your Understanding - Page 834: 42

$900$

The sum of the first $n$ terms of the arithmetic sequence is given by: $S_{n}= \dfrac{n}{2}\left(a_{1}+a_{n}\right)$ We see that there is a constant difference between the terms of $d=2$ The terms of the sum are the first $30$ terms of the arithmetic sequence, starting with $a_{1}=1$ and ending with $a_n=59$ Now, $S_{30}= \dfrac{30}{2}[1+59] \\=(15)(60) \\=900$ Therefore, the sum of the first $n$ terms of the arithmetic sequence is: $900$.