00:02
All righty, so we have a3 is equal to 16 thirds, a5 is equal to 6427, so we're trying to find a7.
00:10
So before we can do that, we need our a1 and our common ratio.
00:13
So we're actually going to have to try and set up a system of equations and substitute in.
00:17
So we're going to start with the a31.
00:20
So i've got 16 thirds is equal to a1, which we don't know, times the ratio, which we don't know.
00:26
But that's going to be to the 3 minus 1 power or squared.
00:30
Then a 5 is going to be 6427th is equal to a 1 times r to the 5 minus 1 power which is going to be to the fourth power so i'll put that so i'm going to do some substitution here i'm going to divide this side by r squared and what that's going to do is that's going to leave me with a 1 equaling 16 over 3 r squared.
01:05
So what i then will do is take that and plug it in for a 1.
01:09
So i'm going to have 64 over 27 is equal to 16 over 3 r squared times r to the fourth.
01:19
So our r squared will cancel and this one will become a 2.
01:23
And then what we'll be able to then do is cross multiply and solve for r...