Answer:
The 8th term is [tex]\frac{1}{729}[/tex].
Step-by-step explanation:
Let's begin with the formula for a geometric sequence. We know this is geometric because we are working with a common ratio, or the number we multiply to find each term.
[tex]a_n=a_0(r)^{n-1}[/tex]
In this formula, [tex]a_0[/tex] is the first term, [tex]r[/tex] is the common ratio, and [tex]n[/tex] is the desired term. We know the values of [tex]r[/tex], [tex]a_0[/tex], and [tex]n[/tex] from the given information:
[tex]a_0=3\\r=\frac{1}{3}\\n=8[/tex]
Substituting those values we get:
[tex]a_8=3(\frac{1}{3})^{8-1}[/tex]
[tex]a_8=3(\frac{1}{3})^7\\a_8=3(\frac{1}{2187})\\a_8=\frac{3}{2187}\\a_8=\frac{1}{729}[/tex]
