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.

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.

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.

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

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

Subtract first from second to get

$\displaystyle S_n=4^{n+1}-4$ so $\displaystyle k=~?.$.

For the next part: I have no idea what " value of of Omega" could mean.

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.

Your answer didn't help at all but thanks anyway.

To Plato:

Thank you for the explanation.

I seem to have a problem with proof questions(even with the easy ones).

I made a silly mistake. In the question they used sigma notation and asked for the value when n=2 and nr of terms=12.

I don't know why I wrote omega. I'm probably just tired :)