Chapter 14 - Sequences, Series, and the Binomial Theorem - 14.2 Arithmetic Sequences and Series - 14.2 Exercise Set - Page 902: 42

$S_{32}=-1200$

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 32nd term first: $a_{n}=a_1+d\times(n-1)$ $a_{32}=9+(-3)\times(32-1)=9-93=-84$ Therefore we can substitute in the formula of the sum, and we get: $S_{32}=\frac{32}{2}\times(9-84)=16\times-75=-1200$