Geometric Sequences -- Forumulas Help

R

ryansanders2002

New member
Joined
Sep 18, 2005
Messages
3
I need help translating a given recursive formula for a geometric sequence into an explicit one.

I know that it is An=A1(r)^n-1. The only problem I have, is my math book gives me two different forms for the recursive. Here are two example problems.

1.) A1=3; An=An-1 + 2; for n>=2
Ok, I assume that 2 is my common ratio? So An=3(2)^n-1 Right?

Now my problem is with this one.

2.)A1=2l; Un=3Un-1; for n>=2.
There is no common ration here(that I see) and whats the deal with the 3?

IS there any easy way to translate these since they don't appear to have a common form?
 
ryansanders2002 said:
1.) A1=3; An=An-1 + 2; for n>=2
Ok, I assume that 2 is my common ratio?
Click to expand...
On what basis do you assume this to be a geometric sequence? Have you found the first four or five terms? Have you found a common ratio?

ryansanders2002 said:
2.)A1=2l; Un=3Un-1; for n>=2.
There is no common ration here(that I see) and whats the deal with the 3?
Click to expand...
"3U<sub>n-1</sub>" means just what it says: "three times the value of the previous term".

Meanwhile, what is "A<sub>1</sub>"? It looks like you have it being set equal to "two times ell", but the variable l is not defined. Also, what is the relation between the A<sub>n</sub>'s and the U<sub>n</sub>'s?

ryansanders2002 said:
IS there any easy way to translate these since they don't appear to have a common form?
Click to expand...
How can you tell what form the terms might have? Have you found any of the terms?

Eliz.
 
My math book just gives those formulas and says write the explicit rule for them. I really have no clue as to whats going on with it. My teacher BRIELFLY went over it and then gave out homework.
Edit:

2.)A1=2; Un=3Un-1; for n>=2.
There is no common ration here(that I see) and whats the deal with the 3?
 
Wait.. Do I actually have to solve these to get the explicit form? I was tring to rewrite the recursive as I would with an arithmetic sequence.
 
I don't know what you mean by "solving" the sequences...?

In order to attempt to find a closed-form expression for the n-th term, you need at least to find a few of the terms.

Eliz.
 
Hello, ryansanders2002!

First of all, these are not necessarily Geometric Sequences.
Evidently, you don't know how to read the notation.

1.) A<sub>1</sub> = 3; A<sub>n</sub> = A<sub>n-1</sub> + 2, . for n <u>></u> 2
.
Click to expand...
First of all, A<sub>n</sub> is the n<sup>th</sup> term of the sequence.

And: A<sub>n-1</sub> is the immediately preceding term.

When it says: . . A<sub>n</sub> .= .A<sub>n-1</sub> + 2
. . . . . . . . . . . . . .↑ . . . . ↑
it means: . n<sup>th</sup> term = preceding term, plus 2

So the sequence is:
. . A<sub>1</sub> .= .3
. . A<sub>2</sub> .= .A<sub>1</sub> + 2 .= .3 + 2 .= .5
. . A<sub>3</sub> .= .A<sub>2</sub> + 2 .= .5 + 2 .= .7
. . A<sub>4</sub> .= .A<sub>3</sub> + 2 .= .7 + 2 .= .9

. . . . . . . and so on.

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

And I assume that #2 still has a typo.

2) U<sub>1</sub> = 2, .U<sub>n</sub> = 3U<sub>n-1</sub>

This one says: . . . . .U<sub>n</sub> .= .3 * U<sub>n-1</sub>
. . . . . . . . . . . . . . . . .↑ . . . . ↑ . . ↑
which means: .nth term .= .3 x preceding term

So the sequence is:
. . U<sub>1</sub> .= .2
. . U<sub>2</sub> .= .3*U<sub>1</sub> .= .3*2 .= .6
. . U<sub>3</sub> .= .3*U<sub>2</sub> .= .3*6 .= .18
. . U<sub>4</sub> .= .3*U<sub>3</sub> .= .3*18 .= .54

. . . . . . . and so on.
 
You must log in or register to reply here.
Top