00:01
In this exercise, we have the first four terms of an infinite sequence, and our goal here is to write out what the nth term, a sub n, must be equal to.
00:10
Well, one commonality between all the terms that we see is, we'll be taking the square root of a particular fraction.
00:18
Next, let's decide what should go in the numerator for this fraction.
00:21
If we ignore the square root sign, then the numerator changes by what appears to be simply adding two to get to each new term in the sequence.
00:31
That means for the numerator, we can start with the base point of 5 that we see here, and write plus n minus 1 times that common difference of 2.
00:46
We're using n minus 1 because we begin indexing at n equals 1.
00:51
In other words, this is a sub 1, a sub 2, and so on down the line.
00:57
So if that's our numerator, we can simplify it to 5 plus 2n minus 1.
01:02
Which is equal to altogether 2n plus 3.
01:07
So let's try out a 2n plus 3 in the numerator...