# How do you find nth term rule for 375,-75,15,-3,....?

Nov 20, 2016

${a}_{n} = 375 \cdot {\left(- \frac{1}{5}\right)}^{n - 1}$

#### Explanation:

Find the nth term rule for: $375 , - 75 , 15 , - 3$...

If you divide any term by the previous term, the quotient is $- \frac{1}{5}$

This indicates the sequence is geometric. In other words, the next term is generated by multiplying the previous term by a fixed number called the common ratio or $r$.

The "formula" for a geometric sequence is ${a}_{n} = {a}_{1} \cdot {r}^{n - 1}$ where $r$ is the common ratio, ${a}_{1}$ is the first term in the sequence, and $n$ is the number of the term in the sequence.

In this example, $r = - \frac{1}{5}$ and ${a}_{1} = 375$

$\implies {a}_{n} = 375 \cdot {\left(- \frac{1}{5}\right)}^{n - 1}$