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: 27

Answer

First five terms are: $a_1 = 11$ $a_2 = 18$ $a_3 = 25$ $a_4 = 32$ $a_5 = 39$ The given sequence is arithmetic with $d=7$.. The $n^{th}$ term is given by the formula: $a_n=11+ 7(n-1)$

Work Step by Step

Find the first five terms by substituting 1, 2, 3, 4 and 5 to $n$ in the given formula. $a_1 = 4+7(1) = 4+7=11$ $a_2 = 4+7(2) = 4+14=18$ $a_3 = 4+7(3) = 4+21=25$ $a_4 = 4+7(4) = 4+28=32$ $a_5 = 4+7(5) = 4+35=39$ A sequence is arithmetic if there exists common difference among consecutive terms. Note that the terms have a common difference of $7$. Thus, the given sequence is arithmetic with $d=7$. The $n^{th}$ term $a_n$ of an arithmetic sequence can be found using the formula $a_n = a+ d(n-1)$ where $d$ = common difference $a$ = first term Since the given arithmetic sequence has $a=11$ and $d=7$, then the $n^{th}$ term is given by the formula: $a_n=11+ 7(n-1)$
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