Chapter 14 - Sequences, Series, and the Binomial Theorem - 14.2 Arithmetic Sequences and Series - 14.2 Exercise Set - Page 902: 28

$n=39$

The n th term of an arithmetic sequence can be calculated as: $a_n=a_1+d\times(n-1)$ Here: $a_{n}=-507$, $a_1=25$, $d=-14$ and we have to find $n$. By substituting we get: $-507=25+(-14)\times(n-1)$ $n-1=\frac{-507-25}{-14}=38$ $n=39$