Math Is Fun Forum

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

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Geometric sequence

Hi;

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

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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...

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- n872yt3r
Math Is Fun Rocks!
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anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

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...

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

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bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Geometric sequence

Hi n872yt3r;

7^2 = 49 and 10^2 = 100

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

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

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