Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 5 - Number Theory and the Real Number System - 5.7 Arithmetic and Geometric Sequences - Exercise Set 5.7: 41

Answer

General formula: $a_n=1+(n-1)(4)$ $a_{20} = 77$

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 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: $a_1 =1$ $d= 5 -1 = 4$ (2) Substitute the values of $a_1$ and $d$ in the general formula given above to find: $a_n= 1 + (n-1)(4)$ Therefore, the 20th term of the sequence is: $a_{20} = 1 + (20-1)(4) \\a_{20} = 1+19(4) \\a_{20} = 1 + 76 \\a_{20} = 77$
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