Finding common ratio, scale factor for Geometric Progression

[Alex12]

Hi there,

I really need some help, about understanding the common ratio and scale factor

The question is: Compute the following and show working:

[tex]\sum_{i=1}^{10} \frac{3^i}{2^i}[/tex]

But I'm not really sure how to find the common ratio, with the fractions and also the scale factor

Can anyone please explain to me how the process works, for finding the common ratio and scale factor??


Thanks

[Guest]

You should know that [tex]\frac{3^i}{2^i}= \left(\frac{3}{2}\right)^i[/tex]. [tex]\left(\frac{3}{2}\right)^{i+1}= \frac{3}{2}\left(\frac{3}{2}\right)^i[/tex] so each term is 3/2 times the previous term. The 3/2 is the "common ratio". I don't know what "scale factor" means here.