Chapter 14 - Sequences, Series, and the Binomial Theorem - 14.2 Arithmetic Sequences and Series - 14.2 Exercise Set - Page 902: 21

$n=57$

The n th term can be calculated as: $a_n=a_1+d\times(n-1)$ Here: $a_n=-328$ and we have to find $n$. In an arithmetic sequence, first we have to find the common difference, which can be calculated as the difference of any two subsequent terms: $d=a_2-a_1=2-8=-6$. By substituting we get: $-328=8+(-6)\times(n-1)$ $n-1=\frac{-328-8}{-6}=56$ $n=57$