Chapter 14 - Sequences, Series, and the Binomial Theorem - 14.2 Arithmetic Sequences and Series - 14.2 Exercise Set - Page 902: 17

$a_{13}=-1628.16$

We have to find the $13$th term of the arithmetic sequence: $1200, 964.32, 728.64,\cdots$ Any term of the arithmetic sequence can be found as $a_n=a_1+d(n-1).$ In our case $a_1=1200$ $d=a_2-a_1=964.32-1200=-235.68$ $n=13.$ Hence the $13$th term is: $a_{13}=1200+(-235.68)(13-1)=-1628.16$