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

1 Answer
Oct 29, 2016

112,224

Explanation:

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

y=7×2x1, 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=7×2x1
y=7×211

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 112and224.

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=147=2814=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=7×2x1