Chapter 5 - Number Theory and the Real Number System - 5.7 Arithmetic and Geometric Sequences - Exercise Set 5.7 - Page 329: 47

General Formula: $a_n=-20+(n-1)(-4)$ $a_{20}=-96$

The formula for the general term (the nth term) of an arithmetic sequence is: $a_n=a_1+(n−1)d$ where d = common difference $a_1$ = first term $a_n$ = nth term n = term number The given arithmetic sequence has: $a_1=-20$ and $d=-4$ Substitute these into the given formula above: $a_n = -20+ (n-1)(-4)$ Thus, $a_{20} = -20+(20-1)(-4) \\a_{20}=-20+19(-4) \\a_{20}=-20+(-76) \\a_{20}=-96$