00:01
We're talking about geometric sequences.
00:02
Geometric sequences are in the form t of n is equal to a times b to the n, where n is our common ratio.
00:14
We know that the difference between an arithmetic sequence is an arithmetic sequence has a constant rate of change, where our geometric sequence is going to have a constant multiplier or a common ratio.
00:30
Now if we're looking at this given geometric sequence, we see that we are doubling.
00:36
And a simple real life situation that i always like to think of for geometric sequences is population.
00:43
If our population is doubling, now we want to find the value of x that will form a geometric sequence.
00:52
So, since i know that for a geometric sequence they have to have the same common ratio, if i take my term and divide it by the term before it, that's going to have to equal another term divided by the term before it.
01:08
I'm going to cross multiply this and solve to get that my x would have to equal 1.
01:14
And then if i plug that in, i'm going to see that my first term, which is 1 plus 2, is 3.
01:22
My second term would be 6...