College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 9 - Section 9.2 - Arithmetic Sequences - 9.2 Assess Your Understanding: 27

Answer

$a_{90} = -266$

Work Step by Step

RECALL: (1) The $n^{th}$ term of an arithmetic sequence can be found using the formula: $a_n = a_1 + (n-1)d$ where $a_1$ = first term and $d$ = common difference (2) The common difference $d$ can be found by subtracting any term to the next term of the sequence: $d=a_n - a_{n-1}$ The given sequence has: $a_1=1$; $d=-2-1=-3$ Substitute these values into the formula for the $n^{th}$ term, we obtain: $a_n=a_1 + (n-1)d \\a_n=1+(n-1)(-3) \\a_n=1+(-3)(n-1) \\a_n=1-3(n-1)$ To find the 90th term, substitute $90$ for $n$ to obtain: $a_{90} = 1-3(90-1) \\a_{90}=1-3(89) \\a_{90}=1-267 \\a_{90} = -266$
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