A geometric sequence is defined recursively by [math]a_n=(a_{n-1})(-\frac{1}{3})[/math], with [math]a_1[/math] = 729. Find the first five terms of the sequence, write an explicit formula to represent the sequence, and find the eighth term.
[list=1] [*]Use the recursive formula to find the first 5 terms of the sequence. [*]The first term is [math]a_1[/math] = 729 and the constant ratio is [math]r=-\frac{1}{3}[/math] , so the explicit formula is [math]a_n=(729)(-\frac{1}{3})^{n-1}[/math]. [*]Substitute 8 in for [math]n[/math] and evaluate. [/list] This applet is provided by Walch Education as supplemental material for the [i]UCSS Secondary Math I[/i] program. Visit [url="http://www.walch.com"]www.walch.com[/url] for more information on our resources.