# The first two terms of a geometric sequence are a1 = 1⁄3 and a2 = 1⁄6. What is a8, the eighth term?

Aug 12, 2016

Use the formula ${t}_{n} = a \times {r}^{n - 1}$

#### Explanation:

Let's first find the value of $r$, the common ratio.

$r = {t}_{2} / {t}_{1}$

$r = \frac{\frac{1}{6}}{\frac{1}{3}}$

$r = \frac{1}{6} \times 3$

$r = \frac{1}{2}$

Now we can us the formula.

${t}_{n} = a \times {r}^{n - 1}$

${t}_{8} = \frac{1}{3} \times {\left(\frac{1}{2}\right)}^{8 - 1}$

${t}_{8} = \frac{1}{8} \times \frac{1}{128}$

${t}_{8} = \frac{1}{1024}$

Hopefully this helps!