College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 8, Sequences and Series - Section 8.2 - Arithmetic Sequences - 8.2 Exercises: 15

Answer

$a_n= \frac{5}{2}-\frac{1}{2}(n-1)$ $a_{10}=2$

Work Step by Step

RECALL: The $n^{th}$ term $a_n$ of an arithmetic sequence can be found using the formula: $a_n = a + d(n-1)$ where $a$ = first term $d$ = common difference $n$ = term number The given arithmetic sequence has $a=\frac{5}{2}$ and $d=-\frac{1}{2}$. This means that the $n^{th}$ term of the sequence is given by the formula: $a_n = \frac{5}{2} + (-\frac{1}{2})(n-1) \\a_n= \frac{5}{2}-\frac{1}{2}(n-1)$ Thus, the 10th term of the sequence is: $a_{10} = \frac{5}{2}-\frac{1}{2}(10-1) \\a_{10}= \frac{5}{2} - \frac{1}{2}(9) \\a_{10} = \frac{5}{2} - \frac{9}{2} \\a_{10} = \frac{5-9}{2} \\a_{10}= -\frac{4}{2} \\a_{10}=2$
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