# What is the n^"th" term of the geometric sequence 360,180,90,45?

Mar 7, 2017

${T}_{n} = 360 \cdot {\left(\frac{1}{2}\right)}^{n - 1}$

#### Explanation:

A GP has the general term ${T}_{n} = a {r}^{n - 1}$

In this case we have:

${T}_{1} = a = 360$

$r = {T}_{n} / {T}_{n - 1} = \frac{45}{90} = \frac{90}{180} = \frac{180}{360} = \frac{1}{2}$

Substituting these values gives: ${T}_{n} = 360 \cdot {\left(\frac{1}{2}\right)}^{n - 1}$

This means that if we want to know the value of a particular term, we just need to plug in the value of $n$.