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: 29

Answer

$a_{80}=\frac{83}{2}$

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: $a_1=2$; $d=\frac{5}{2} - 2 = \frac{5}{2} - \frac{4}{2} = \frac{1}{2}$ Substitute these values into the formula for the $n^{th}$ term to obtain: $a_n=a_1 + (n-1)d \\a_n=2+(n-1)(\frac{1}{2}) \\a_n=2+\frac{1}{2}(n-1)$ To find the 80th term, substitute $80$ for $n$ to obtain: $a_{80} = 2+\frac{1}{2}(80-1) \\a_{80}=2+\frac{1}{2}(79) \\a_{80}=2+\frac{79}{2} \\a_{80} =\frac{4}{2}+\frac{79}{2} \\a_{80}=\frac{83}{2}$
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