# Math Help - Geometric Sequences and Series

1. ## Geometric Sequences and Series

Q. If Un of the sequence 2, 4, 8,... is 512, find n.

Eq.: Un = ar^n-1

Attempt:
Un = ar^n-1
2.2^n-1 = 512
n = 9

My question is, can n be solved without randomly subbing values into n? Thank you.

2. ## Re: Geometric Sequences and Series

you can use logarithms

3. ## Re: Geometric Sequences and Series

Originally Posted by GrigOrig99
Q. If Un of the sequence 2, 4, 8,... is 512, find n.

Eq.: Un = ar^n-1

Attempt:
Un = ar^n-1
2.2^n-1 = 512
n = 9

My question is, can n be solved without randomly subbing values into n? Thank you.
the author of these "formulated" problems expects that the student knows

$512 = 2^9$

4. ## Re: Geometric Sequences and Series

Originally Posted by waqarhaider
[Tex]\mbox{you\can\use\logarithms[\Tex]
I don't think GrigOrig99 has already learned logarithms.

5. ## Re: Geometric Sequences and Series

Originally Posted by GrigOrig99
Q. If Un of the sequence 2, 4, 8,... is 512, find n.

Eq.: Un = ar^n-1

Attempt:
Un = ar^n-1
2.2^n-1 = 512
n = 9

My question is, can n be solved without randomly subbing values into n? Thank you.
$u_1=2=2^1$

$u_2=4=2^2$

$u_3=8=2^3$

$u_n=2^n$

If you wish, you may keep doubling until you reach 512

$u_4=16,\;\;\;u_5=32,\;\;\;u_6=64....\;\;etc$

6. ## Re: Geometric Sequences and Series

Apologies if I was unclear. I understand why n = 9, i.e. 2^9 = 512. What I meant was whether or not 9, itself, can be calculated from just:

2.2^n-1 = 512

I don't believe it's possible but just wanted to double check with you guys. Thanks again.

7. ## Re: Geometric Sequences and Series

You may use the Power Law of logarithms.

$2^n=512\Rightarrow\ log2^n=log512$

Now use

$loga^b=bloga$

$nlog2=log512$

$n=\frac{log512}{log2}$

Natural logs or "logs to base 10" may be used.

8. ## Re: Geometric Sequences and Series

Thank you for clearing that up. I'm getting better at doing most of these sums on my own, slowly but surely.

9. ## Re: Geometric Sequences and Series

Sorry, then I've to take back what I said about that you haven't learnt logarithms yet .