Find common ratios of geometric sequences

This video shows how to find the common ratio when given a geometric series.

[collegealgebra]

+Awesome Iris
If you know that it is a geometric sequence, then you can utilize a similar method for finding the common ratio.

Suppose that we use the same sequence, but are told that the first number (a0) is 2 and the third number (a2) is 50. We're not told what a1 is, which makes it just a little bit harder, but not impossible.

Our ratio is a2/a0=50/2=25. But, remember, since this is a geometric sequence, we have multiplied by the same thing twice. This means that we have some unknown common ratio, let's say r, that is being multiplied twice, so we have r^2=25. We can solve this for r by taking the square root of both sides (and using the Square Root property) to get r=5 or r=-5. Please note that in order to figure out which one it is, we need at least one more number in the sequence.

As a point of fact, if they ever give you two numbers in the sequence adjacent to each other, simply divide the latter one by the earlier one, and you'll find your ratio. Using 1250 and 250 from this sequence as an example gives: 1250/250=5, which is the same ratio.

[the.legit.batman]

but what if they only give you the first and third term