College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 8, Sequences and Series - Section 8.2 - Arithmetic Sequences - 8.2 Exercises - Page 607: 16


$a_n=\sqrt3(n)$ $a_{10}= 10\sqrt3$

Work Step by Step

RECALL: The $n^{th}$ term $a_n$ of an arithmetic sequence can be found using the formula: $a_n = a + d(n-1)$ where $a$ = first term $d$ = common difference $n$ = term number The given arithmetic sequence has $a=\sqrt3$ and $d=\sqrt3$. This means that the $n^{th}$ term of the sequence is given by the formula: $a_n = \sqrt3 + \sqrt3(n-1) \\a_n= \sqrt3[1+(n-1)] \\a_n=\sqrt3(1+n-1) \\a_n=\sqrt3(n)$ Thus, the 10th term of the sequence is: $a_{10} = \sqrt3(10) \\a_{10}= 10\sqrt3$
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