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 - Page 654: 20


$a_n=6-2(n-1)$ $a_{51} = -94$

Work Step by Step

RECALL: 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 The given sequence has: $a_1=6$; $d=-2$ Substitute these values into the formula for the $n^{th}$ term to obtain: $a_n=a_1 + (n-1)d \\a_n=6+(n-1)(-2) \\a_n=6+(-2)(n-1) \\a_n=6-2(n-1)$ To find the 51st term, substitute $51$ for $n$ to obtain: $a_{51} = 6-2(51-1) \\a_{51}=6-2(50) \\a_{51} =6-100 \\a_{51} = -94$
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