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## #1 2013-01-29 14:55:32

3rdMath
Member
Registered: 2013-01-29
Posts: 1

### Geometric sequence

Given the series 1/2 + 1/(2^4)+1/(2^7)+1/(2^10)
(i) show that this is geometric sequence..........can some1 help with this please

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## #2 2013-01-29 15:29:33

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 106,362

### Re: Geometric sequence

Hi;

That is a geometric series because each term has a common ratio which is

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
No great discovery was ever made without a bold guess.

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## #3 2013-01-29 23:45:13

n872yt3r
Member
Registered: 2013-01-21
Posts: 392

### Re: Geometric sequence

(2^4=16) (2^7=49) (2^10=100) 1/16+1/49=0.0829081632653061224489795183673...+1/100=0.09290816326530612244897959183673...+1/2=0.59290816326530612244897959183673...

- n872yt3r
Math Is Fun Rocks!
By the power of the exponent, I square and cube you!

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## #4 2013-01-30 02:20:27

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,018

### Re: Geometric sequence

n872yt3r wrote:

(2^4=16) (2^7=49) (2^10=100) 1/16+1/49=0.0829081632653061224489795183673...+1/100=0.09290816326530612244897959183673...+1/2=0.59290816326530612244897959183673...

That is not correct. 2^7 is not 49 and 2^10 is not 100...

Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
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## #5 2013-01-30 02:25:14

bobbym
From: Bumpkinland
Registered: 2009-04-12
Posts: 106,362

### Re: Geometric sequence

Hi n872yt3r;

7^2 = 49 and 10^2 = 100

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
No great discovery was ever made without a bold guess.

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## #6 2013-01-30 03:51:26

mttal24
Member
Registered: 2012-05-01
Posts: 23

### Re: Geometric sequence

Well, to identify and prove a geometric progression the following can be used:
If
t2/t1=t3/t2=t4/t3=.....=tn/t(n-1)=r  (and 'r' also represents common ratio)
then the sequence is a GP.
Here,
1/2^4 divided by1/2 is equal to 1/2^7 divided by 1/2^4.
Thus, you can show that it is a gp

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## #7 2013-01-30 04:01:28

bob bundy
Moderator
Registered: 2010-06-20
Posts: 7,705

### Re: Geometric sequence

hi 3rdMath

Welcome to the forum.

If you had an algebraic form for the general term, then you could do the job in one go with

As you have just 4 terms and no general term you will have to show that

The value for this constant has already been given in earlier posts.

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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