00:01
In this sequence, the nth term is equal to 2 to the n power divided by 3 to the n minus 1 power.
00:06
So, let's determine its common ratio if it is in fact geometric.
00:10
Well, to find out if it's geometric, we just need to find if there's a common ratio.
00:15
So in finding the common ratio, we will determine if it's geometric or not.
00:19
Let's get started.
00:20
Common ratio is equal to one term divided by the previous, such as 2 to the n over 3 to the n minus 1, divided by, 2 to the n minus 1 over 3 to the n minus 2.
00:35
We can multiply this fraction up to make it easier to look at.
00:39
That will give us 3 to the n minus 2 times 2 to the n, divided by 3 to the n minus 1 times 2 to the n minus 1.
00:50
And now we can use a well -known exponent rule, which allows us to turn division into subtraction of exponents.
00:57
That is, we now have 3 to the n minus 2 minus n minus 1 times 2 to the n minus n minus 1.
01:09
This will equal while we have this 3 raised to the n minus n is just 0, and the negative 2 minus negative 1 comes up to negative 1, times 2 raised to the n minus n is 0, and then minus minus 1 is positive 1...