# What are the next two numbers in the pattern, 5, -10, -20, -40?

Dec 17, 2017

Expanding on the idea...

#### Explanation:

We can also formulate this

This is called a geometric sequence, where the next term can be obtained by multiplying the prior term by a paricular number, called a common ration...

So if $a$ is our first term, and $r$ is our common ration, then our sequence would look like...

$a , a r , a {r}^{2} , a {r}^{3.} \ldots$

This has an $n t h$ term of: $a \cdot {r}^{n - 1}$ where the first term is at $n = 1$

$- 5 , - 10 , - 20 , - 40. . .$

So $a = - 5 \mathmr{and} r = 2$

$n t h$ term = $\left(- 5\right) \cdot {2}^{n - 1}$

So our next terms our $n = 5$ and then $n = 6$

So hecne using the formula: -80, -160 are the next two terms

We can also take a sum of the first $n$ terms, but thats a different story...!