# What is the nth term of the geometric sequence 2,10,50,250?

Feb 15, 2016

Use the explicit formula for a geometric sequence:

${a}_{n} = {a}_{1} {\left(r\right)}^{n - 1}$

#### Explanation:

First, find the common ratio $r = \frac{10}{2} = 5$

Now, insert the values from the problem into the explicit formula ...

${a}_{n} = 2 {\left(5\right)}^{n - 1}$

So, for example if you want to know the 11th term ...

${a}_{11} = 2 {\left(5\right)}^{\left(11 - 1\right)} = 19 , 531 , 250$ [wow! that's a big number!]

Hope that helped!