Question

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

Answer 1

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,ar,ar^2,ar^3....`

This has an `nth` term of: `a*r^(n-1)` where the first term is at `n=1`

Your sequance is:

`-5,-10,-20,-40...`

So `a = -5 and r = 2`

`nth` term = `(-5)*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...!