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: 12

Answer

$a_n = -5 + 4(n-1)$ $a_{10} = 31$

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 $a=-5$ and $d=4$. This means that the $n^{th}$ term of the sequence is given by the formula: $a_n = -5 + 4(n-1)$ Thus, the 10th term of the sequence is: $a_{10} = -5+4(10-1) \\a_{10}=-5+4(9) \\a_{10} = -5+36 \\a_{10} = 31$
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