# Geometric series question (proof) C2

• Mar 3rd 2013, 08:47 AM
Tuzina
Geometric series question (proof) C2
Hi everyone,
I have a question from GeometricSeries(c2) and I'm stuck on (c)(i).
The nth term of a geometric sequence is Un, where Un=3x4^n
(a) Find the value of U1 and show that u2=48
(b) Wriste down the common ratio of the geometric sequence.
(c) (i) Show that the sum of the first 12 terms of the geometric sequence is 4^k - 4where k is an integer
(ii) Hence find value of of Omega with 12 terms and first term n=2 Un.
• Mar 3rd 2013, 09:26 AM
MINOANMAN
Re: Geometric series question (proof) C2
Tuzina

it seems to me that you didn;t study at all G.S and you want us to solve your H.W.
your questions are so easy for someone who has study the G.S that he would feel shame to ask such questions.
if you apply the folrmulae of the G.P your questions will be solved easily.

Please revise the G.P and GS.
• Mar 3rd 2013, 09:39 AM
Plato
Re: Geometric series question (proof) C2
Quote:

Originally Posted by Tuzina
Hi everyone,
I have a question from GeometricSeries(c2) and I'm stuck on (c)(i).
The nth term of a geometric sequence is Un, where Un=3x4^n
(c) (i) Show that the sum of the first 12 terms of the geometric sequence is 4^k - 4where k is an integer
(ii) Hence find value of of Omega with 12 terms and first term n=2 Un.

$S_n=3\cdot 4^1+3\cdot 4^2+\cdots +3\cdot 4^n$
$4\cdot S_n=3\cdot 4^2+3\cdot 4^3+\cdots +3\cdot 4^{n+1}$

Subtract first from second to get
$S_n=4^{n+1}-4$ so $k=~?.$.

For the next part: I have no idea what " value of of Omega" could mean.
• Mar 3rd 2013, 10:10 AM
Tuzina
Re: Geometric series question (proof) C2
To MINOANMAN:
I studied GS and I know the formulas. Yes, this is my HW.
Yes. This question is probably easy but it doesn't change a fact that I don't know how to do it.
No. I'm not ashamed to ask easy/stupid questions because I always learn something new even from these.
If I apply the formulae it will be solved. TRUE.