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: 25

Answer

$a_{100} = 200$

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 from the next term of the sequence: The given sequence has: $a_1=2$; $d=4-2=2$ Substitute these values into the formula for the $n^{th}$ term, we obtain: $a_n=a_1 + (n-1)d \\a_n=2+(n-1)2$ To find the 100th term, substitute $100$ for $n$ to obtain: $a_{100} = 2+(100-1)(2) \\a_{100}=2+99(2) \\a_{100}=2+198 \\a_{100} = 200$
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