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: 38

Answer

$a_{14}=11\frac{1}{4}$

Work Step by Step

The nth term of an arithmetic sequence can be found using the formula: $a_n=a_1+(n−1)d$ where d = common difference $a_1$ = first term $a_n=n^{th}$ term The given arithmetic sequence has: $a_1=8 \\d=\frac{1}{4}$ Use the formula above to find the 14th term: $a_n=a_1+(n−1)(d) \\a_{14}=8+(14−1)(\frac{1}{4}) \\a_{14}=8+13(\frac{1}{4}) \\a_{14}=8+\frac{13}{4} \\a_{14}=8+3\frac{1}{4} \\a_{14}=11\frac{1}{4}$
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