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: 37

Answer

$a_{12}=11.5$

Work Step by Step

The $n^{th}$ term of an arithmetic sequence can be found using the formula: $a_n=a_1+(nāˆ’1)d$ where d = common difference $a_1$ = first term $a_n$=$n^{th}$ term The given arithmetic sequence has: $a_1=6 \\d=\frac{1}{2}$ Use the formula above to find the 12th term: $a_n=a_1+(nāˆ’1)(d) \\a_{12}=6+(12-1)(\frac{1}{2}) \\a_{12}=6+11(\frac{1}{2}) \\a_{12}=6+(\frac{11}{2}) \\a_{12}=6+5.5 \\a_{12}=11.5$
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