Question

What are the next two numbers in the pattern: 7, 14, 28, 56?

Answer 1

`112, 224`

Explanation:

This is a geometric sequence. Its exponential growth model is:

`y=7xx2^(x-1)`, where `x` is the number of the term in the sequence (1st, 17th, etc), plotted on the x-axis.

`y` is the number that occupies that term (The 1st term is 7, etc).
So lets plug in some values:

For the first term: `x = 1`
`y=7xx2^(x-1)`
`y=7xx2^(1-1)`

Because anything to the power of 0 is 1, this ends up being 7.

This equation works for any of the terms. Plug in 5 and 6 for the term numbers `(x)` and you get `112 and 224.`

If you prefer a simpler approach which is good for nice round numbers like these, just notice that it is doubling every time, starting with 7. Double a term and you get the next.

Here is how to find the model for a sequence like this:

Divide one term by the previous one to find the common ratio.

In this case, it's 2. `" "r = 14/7 =28/14 =2`

Assume the first term is where `x=1` unless told otherwise. If it isn't the first term, go backward dividing by the common ratio until you get to the first term/x=1. The first term here is 7.

Then plug it into the formula:
`y=7xx2^(x-1)`