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: 22

Answer

$a_n=1-\frac{1}{3}(n-1)$ $a_{51}=-\frac{47}{3}$

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: $a_1=1$; $d=-\frac{1}{3}$ Substitute these values into the formula for the $n^{th}$ term to obtain: $a_n=a_1 + (n-1)d \\a_n=1+(n-1)(-\frac{1}{3}) \\a_n=1+(-\frac{1}{3})(n-1) \\a_n=1-\frac{1}{3}(n-1)$ To find the 51st term, substitute $51$ for $n$ to obtain: $a_{51} = 1-\frac{1}{3}(51-1) \\a_{51}=1-\frac{1}{3}(50) \\a_{51} = 1-\frac{50}{3} \\a_{51} = \frac{3}{3}-\frac{50}{3} \\a_{51}=-\frac{47}{3}$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.