# The lengths of the sides in a right triangle form 3 consecutive terms of a geometric sequence. How do you find the common ratio of the sequence?

##### 1 Answer

The ratio must be

#### Explanation:

Three numbers are in a geometric series if they're of the form

If they're sides of a right triangle, then we have

which is

Simplifying by

To solve this equation (which of course you can rewrite as

And this equation is quite famous, since it is the one whose solution involve the golden ratio, so

Now we have to remember that

Finally, we can solve for