For the following sequence, determine the indicated geometric means;
180,_,_,_,_,-5.625,...
I could hardly even calculate this! Anyone have a better idea?
180x(r^5)=-5.625
r^5= -0.03125
r=-1/2
so the sequence is
180,-90,45,-22.5,11.25,-5.625
Now, the geometric mean is all those multiplied together, then the sixth root of that: Note this is impossible to take the sixth root of negative number and get a real number. Technically, that sequence has no geometric mean.
To find the indicated geometric means in the given sequence, we need to calculate the common ratio between consecutive terms. Once we find the common ratio, we can use it to calculate the missing terms.
In this case, we have the sequence: 180, _, _, _, _, -5.625.
Let's start by finding the common ratio between consecutive terms. To do this, we divide each term by its preceding term.
Common ratio (r) = Term(n) / Term(n-1)
For the given sequence, let's find the common ratio between the first two terms:
r = Term(2) / Term(1) = _ / 180
To find the missing term after 180, we can assume a value for the common ratio (r) since we don't have any other information.
Let's assume r = 2.
To find the second term, we multiply the first term by the common ratio:
Term(2) = Term(1) * r = 180 * 2 = 360.
The second term is 360.
To find the third term, we multiply the second term by the common ratio:
Term(3) = Term(2) * r = 360 * 2 = 720.
The third term is 720.
To find the fourth term, we again multiply the third term by the common ratio:
Term(4) = Term(3) * r = 720 * 2 = 1440.
The fourth term is 1440.
Finally, to find the fifth term, we multiply the fourth term by the common ratio:
Term(5) = Term(4) * r = 1440 * 2 = 2880.
The fifth term is 2880.
Now, we have the sequence: 180, 360, 720, 1440, 2880, -5.625.
So, the indicated geometric means are 360, 720, 1440, and 2880.