Question

Find the 8th term of the sequence whose common ratio is 1/3 and whose first term is 3

Answer 1

Answer:

The 8th term is $\frac{1}{729}$.

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.

$a_n=a_0(r)^{n-1}$

In this formula, $a_0$ is the first term, $r$ is the common ratio, and $n$ is the desired term. We know the values of $r$, $a_0$, and $n$ from the given information:

$a_0=3\\r=\frac{1}{3}\\n=8$

Substituting those values we get:

$a_8=3(\frac{1}{3})^{8-1}$

$a_8=3(\frac{1}{3})^7\\a_8=3(\frac{1}{2187})\\a_8=\frac{3}{2187}\\a_8=\frac{1}{729}$