Question

3 A motor has 5 speeds varying from X rpm to Y rpm in a Geometric Progression.                                                                  

Calculate the common ratio

Make a table of the speeds.

Answer 1

Initial Speed = x

Final Speed = y

Say the geometric ratio = r

In case of geometric progression, the above case be represented as

$x, xr, xr^2, xr^3, xr^4, , xr^5, y$

Therefore, it can be said that

$x r ^5 = y$

Therefore,

$r^5 = \frac{y}{x}$

Or, $r = (\frac{y}{x})^{1/5}$

Therefore, the common ratio is given by: $r = (\frac{y}{x})^{1/5}$