# Thread: Stuck on Geometric Progressions

1. ## Stuck on Geometric Progressions

Hey all. Im new here but I thought that you might be able to help me figure out what I am doing wrong here.

Im doing Geometric Progressions for my final school year, and where on holidays (got some homework). Anyway Im stuck at the end of an excercise. Here is one of the questions.

Find the value of n if the sum of n terms of the series 11 + 33 + 99 + ... is equal to 108251.

Ok I get that a=11, r=3, and Sn=108251

And you put this into

Sn= a(r^n -1) / (r -1)

But I just do something wrong from there.

Thankyou very much.

2. ## Re :

It seems that you are right . .

$\displaystyle \frac{11(3^n-1)}{3-1}=108251$

$\displaystyle 3^n=19683$

$\displaystyle n=\frac{In 19683}{In 3}$

3. ## Thanks

Yeh that works .

We havent learnt intergration yet. So its a tad confusing.

And in the worked examples they will simplify the total on one side so that it is is in the same format.

An example is (a worked example)..

The sum of n terms of 1 + 4 + 16 ... 21845. Find the value of n.

Sol. a=1, r=4, Sn=21845

21845= 1(4^n -1) / (4-1)
= 4^n -1 / 3
65535= 4^n -1
65536= 4^n
4^8= 4^n

Therefore n=8

I cant understand how to do it this way..

4. Originally Posted by TickyTock
Yeh that works .

We havent learnt intergration yet. So its a tad confusing.

And in the worked examples they will simplify the total on one side so that it is is in the same format.

An example is (a worked example)..

The sum of n terms of 1 + 4 + 16 ... 21845. Find the value of n.

Sol. a=1, r=4, Sn=21845

21845= 1(4^n -1) / (4-1)
= 4^n -1 / 3
65535= 4^n -1
65536= 4^n
4^8= 4^n

Therefore n=8

I cant understand how to do it this way..

It is the same ,just substitute a and r into the formula ..

or do u mean something else ?

5. ## Hmm

I think I figured out what i was doing wrong.

I wont expand the top line untill everything is taken to the other side, cause that didnt work.

Also is intergration the only way that you could find out what to make n (without guesswork).

65536= 4^n

4^8= 4^n

Thankyou very much

6. ## RE:

NO !!!!!!!! , that's not integration , In is a natural logarithms . Sorry for the confusion . Have you learnt about $\displaystyle log_{10}$

u can solve it this way too , $\displaystyle \frac{log_{10}{19683}}{log_{10}{3}}$

7. ## umm..

I dont think we have.

I will use In. As it works even though im not sure what it means or does. But ill be sure to ask my maths teacher when I get back to school, She will help me Just have to get this done for now.

Also I was wondering what program or site you used to write all of those maths equations properally on the computer. It would be useful for in the future when i need more help.

Thanks heaps

8. ## Re :

Originally Posted by TickyTock
I dont think we have.

I will use In. As it works even though im not sure what it means or does. But ill be sure to ask my maths teacher when I get back to school, She will help me Just have to get this done for now.

Also I was wondering what program or site you used to write all of those maths equations properally on the computer. It would be useful for in the future when i need more help.

Thanks heaps

Well , you need to check out these topics ( indices and logarithms ) .
About the math equations , this forum has latex installed . You can check out the latex tutorial , http://www.mathhelpforum.com/math-help/latex-help/ .