# How do you write a rule for the nth term of the geometric term and then find a_6 given r=1/10, a_2=4?

Mar 10, 2017

${T}_{6} = \frac{1}{2500} = 0.0004$

#### Explanation:

In a GP, each term is multiplied by the common ratio to get the next term in the sequence.

We do not have the first term, $a$, but we can find it from ${T}_{2}$

${T}_{2} = 4 = a \times \frac{1}{10}$

$a = 4 \times 10 = 40$

${T}_{n} = a {r}^{n - 1}$

${T}_{n} = 40 \cdot {\left(\frac{1}{10}\right)}^{n - 1}$

${T}_{6} = 40 \cdot {\left(\frac{1}{10}\right)}^{5}$

$T - 6 = 40 \times \frac{1}{10} ^ 5$

${T}_{6} = \frac{1}{2500} = 0.0004$