# Chapter 5 - Number Theory and the Real Number System - 5.7 Arithmetic and Geometric Sequences - Exercise Set 5.7: 46

General Formula: $a_n=6+(n-1)(3)$ $a_{20} = 63$

#### Work Step by Step

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: $a_1=6$ and $d=3$ Substitute these into the given formula above: $a_n = 6 + (n-1)(3)$ Thus, $a_{20} = 6+(20-1)(3) \\a_{20}=6+19(3) \\a_{20}=6+57 \\a_{20}=63$

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