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: 31

Answer

The first five terms are: $a_1 = -4$ $a_2 = 2$ $a_3 = 8$ $a_4 = 14$ $a_5 = 20$ The sequence is arithmetic with $d=6$. The $n^{th}$ term $a_n$ is given by the formula: $a_n=-4 + 6(n-1)$

Work Step by Step

Find the first five terms by substituting 1, 2, 3, 4 and 5 to $n$ in the given formula. $a_1 = 6(1) - 10 = 6-10 = -4$ $a_2 = 6(2)-10 = 12-10 = 2$ $a_3 = 6(3)-10 = 18-10 =8$ $a_4 = 6(4)-10 = 24-10 = 14$ $a_5 = 6(5)-10=30-10 = 20$ A sequence is arithmetic if there exists common difference among consecutive terms. Note the consecutive terms increase by $6$. Thus, the sequence is arithmetic with $d=6$. The $n^{th}$ term $a_n$ of the sequence, whose $a=-4$ and $d=6$, is given by the formula: $a_n=-4 + 6(n-1)$
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