Difficult question which involves a geometric series (1 Viewer)

[nicholas101]

I'm finishing off holiday work assigned to me before school starts back and I find myself stuck on this question all the time:
"In any GP, let Rn = T(n + 1) + T(n + 2) + ... + T(2n). Show that Rn:Sn = r^n:1, and hence find r if R8:S8 = 1:81"

This is how the question is printed in my textbook. I've tried to think about how this question has been answered and I've heard that most of my friends in my grade have not been able to solve this question.
If you could provide any worked solutions, I would appreciate it!
Thanks!

 

[Drdusk]

I'm finishing off holiday work assigned to me before school starts back and I find myself stuck on this question all the time:
"In any GP, let Rn = T(n + 1) + T(n + 2) + ... + T(2n). Show that Rn:Sn = r^n:1, and hence find r if R8:S8 = 1:81"

This is how the question is printed in my textbook. I've tried to think about how this question has been answered and I've heard that most of my friends in my grade have not been able to solve this question.
If you could provide any worked solutions, I would appreciate it!
Thanks!

What’s Sn?

 

[nicholas101]

What’s Sn?

Sn is meant to be the symbol of the sum of the first n terms of a GP (a + ar + ar^2 + ...)

 

[Trebla]

If you write out R_n explicitly using the general terms of a GP you should notice that you can factorise rⁿ. From that point the rest should follow.

 

[Drongoski]