Finding the ratio of the geometric sequence?

• Mar 10th 2009, 11:59 AM
puzzledwithpolynomials
Finding the ratio of the geometric sequence?
i, -1, i
So the ratio if sqrt(-1)/-1? There doesn't seem to be a common ratio...
• Mar 10th 2009, 01:22 PM
Prove It
Quote:

Originally Posted by puzzledwithpolynomials
i, -1, i
So the ratio if sqrt(-1)/-1? There doesn't seem to be a common ratio...

$\frac{t_2}{t_1} = \frac{i}{-1} = -i$.

$\frac{t_3}{t_2} = \frac{-1}{i} = \frac{-1}{i}\cdot\frac{-i}{-i} = \frac{-(-i)}{-i^2} = \frac{i}{-(-1)} = \frac{i}{1} = i$.

You're right, there's not a common ratio.
• Mar 10th 2009, 02:00 PM
Plato
Quote:

Originally Posted by puzzledwithpolynomials
i, -1, i
So the ratio if sqrt(-1)/-1? There doesn't seem to be a common ratio...

As written, I must agree with you. It is no geometric.

If it were $i\;,\, - 1\;,\, \color{red}{- i}$ then $i$ works.