For the following sequence, determine the indicated geometric means;

180,_,_,_,_,-5.625,...
I could hardly even calculate this! Anyone have a better idea?

1 answer

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.