# How do you find the next three terms of the sequence 2,10,50,250,1250,...?

May 17, 2018

See below

#### Explanation:

We are dealing with a geometric squence of ratio 5.

$\frac{10}{2} = 5$; $\frac{50}{10} = 5$; $\frac{250}{50} = 5$ etc...

We know general term is given by ${a}_{n} = {a}_{1} {r}^{n - 1}$ with ${a}_{1} = 2$ and $r = 5$

In our case a_n=2·5^(n-1)

Now for

$n = 6$ a_6=2·5^5=6250
$n = 7$ a_7=2·5^6=31250
$n = 8$ a_8=2·5^7=156250