# Chapter 5 - Number Theory and the Real Number System - 5.7 Arithmetic and Geometric Sequences - Exercise Set 5.7 - Page 329: 44

General Formula: $a_n=6+(n-1)(-5)$ $a_{20}=-89$

#### Work Step by Step

RECALL: 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 To find the formula for the general term, perform the following steps: (1) Find the values of $a_1$ and $d$ The given sequence has: $a_1 =6$ $d= 1 -6 = -5$ (2) Substitute the values of $a_1$ and $d$ in the general formula given above to find: $a_n= 6+ (n-1)(-5)$ Therefore, the 20th term of the sequence is: $a_{20} = 6 + (20-1)(-5) \\a_{20} = 6+19(-5) \\a_{20} = 6+ (-95) \\a_{20} = -89$

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