# Thread: Geometric Sequences + Irrational Numbers

1. ## Geometric Sequences + Irrational Numbers

Question:
find the general term of Un which as
u3=3 and u9=3/8

--> i am looking for the common ratio atm and this is what i did
u3=u1r^2=3 (1)
u9=u1r^(-5/8)=3/8 (2)

--> (2)/(1)
u1r^(-5/8)/ u1r^2 =3/8 / 3

r^(-21/8) = 1/8

r = (-21/8)* root 1/8

But i don't know how to simplify it from there..

but i don't know how to get that

thank you

2. Originally Posted by juliak
Question:
find the general term of Un which as
u3=3 and u9=3/8

--> i am looking for the common ratio atm and this is what i did
u3=u1r^2=3 (1)
u9=u1r^(-5/8)=3/8 (2)

--> (2)/(1)
u1r^(-5/8)/ u1r^2 =3/8 / 3

r^(-21/8) = 1/8

r = (-21/8)* root 1/8

But i don't know how to simplify it from there..

but i don't know how to get that

thank you
$\displaystyle u_3 = a r^2$ and $\displaystyle u_9 = a r^8$. Therefore:

$\displaystyle \frac{u_9}{u_3} = r^6 = \frac{3/8}{3}\Rightarrow r^6 = \frac{1}{8} \Rightarrow r^6 = \frac{1}{2^3} = ....$

3. u9=a1r^-5/8?

how does u9=a1r^8?

4. Originally Posted by juliak
u9=a1r^-5/8?

how does u9=a1r^8?
Didn't you say it's a geometric series.

You're expected to know that the nth term is given by $\displaystyle u_n = a r^{n-1}$.

I have absolutely no idea where you're getting u9=a1r^-5/8 from.

5. oh >_<

but umm i stil don't really get how to simplify
r^6 = 1/2^3
why do you have to change 8 to 2^3 and what do you do to continue simplifying it?

6. Originally Posted by juliak
oh >_<

but umm i stil don't really get how to simplify
r^6 = 1/2^3
why do you have to change 8 to 2^3 and what do you do to continue simplifying it?
You should go back and review all the material (like index laws) that this question clearly implies you should already know.

$\displaystyle r^6 = \frac{1}{2^3} \Rightarrow r = \left( \frac{1}{2^3} \right)^{1/6} = \frac{1}{(2^3)^{1/6}} = \frac{1}{2^{1/2}} = \frac{1}{\sqrt{2}}$.
The text passage contains a mathematical question about finding the common ratio of a geometric sequence, and it includes a detailed attempt to solve the problem. The solution is partially provided in the subsequent posts, but not fully completed within the text.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# Thread: Geometric Sequences + Irrational Numbers

1. ## Geometric Sequences + Irrational Numbers

Question:
find the general term of Un which as
u3=3 and u9=3/8

--> i am looking for the common ratio atm and this is what i did
u3=u1r^2=3 (1)
u9=u1r^(-5/8)=3/8 (2)

--> (2)/(1)
u1r^(-5/8)/ u1r^2 =3/8 / 3

r^(-21/8) = 1/8

r = (-21/8)* root 1/8

But i don't know how to simplify it from there..

but i don't know how to get that

thank you

2. Originally Posted by juliak
Question:
find the general term of Un which as
u3=3 and u9=3/8

--> i am looking for the common ratio atm and this is what i did
u3=u1r^2=3 (1)
u9=u1r^(-5/8)=3/8 (2)

--> (2)/(1)
u1r^(-5/8)/ u1r^2 =3/8 / 3

r^(-21/8) = 1/8

r = (-21/8)* root 1/8

But i don't know how to simplify it from there..

but i don't know how to get that

thank you
$\displaystyle u_3 = a r^2$ and $\displaystyle u_9 = a r^8$. Therefore:

$\displaystyle \frac{u_9}{u_3} = r^6 = \frac{3/8}{3}\Rightarrow r^6 = \frac{1}{8} \Rightarrow r^6 = \frac{1}{2^3} = ....$

3. u9=a1r^-5/8?

how does u9=a1r^8?

4. Originally Posted by juliak
u9=a1r^-5/8?

how does u9=a1r^8?
Didn't you say it's a geometric series.

You're expected to know that the nth term is given by $\displaystyle u_n = a r^{n-1}$.

I have absolutely no idea where you're getting u9=a1r^-5/8 from.

5. oh >_<

but umm i stil don't really get how to simplify
r^6 = 1/2^3
why do you have to change 8 to 2^3 and what do you do to continue simplifying it?

6. Originally Posted by juliak
oh >_<

but umm i stil don't really get how to simplify
r^6 = 1/2^3
why do you have to change 8 to 2^3 and what do you do to continue simplifying it?
You should go back and review all the material (like index laws) that this question clearly implies you should already know.

$\displaystyle r^6 = \frac{1}{2^3} \Rightarrow r = \left( \frac{1}{2^3} \right)^{1/6} = \frac{1}{(2^3)^{1/6}} = \frac{1}{2^{1/2}} = \frac{1}{\sqrt{2}}$.
user
The text passage contains a mathematical question about finding the common ratio of a geometric sequence, and it includes a detailed attempt to solve the problem. The solution is partially provided in the subsequent posts, but not fully completed within the text.

TYPE: SINGLE_QUESTION_WITH_ANSWER