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# The geometric series a+ar+ar^2............. has a sum of 7,

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Current Student
Joined: 11 May 2008
Posts: 552
The geometric series a+ar+ar^2............. has a sum of 7, [#permalink]

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08 Aug 2008, 04:47
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The geometric series a+ar+ar^2............. has a sum of 7, and the terms involving odd powers of r have a sum of 3. What is a+r?

4/3
12/7
3/2
7/3
5/2

mention how long it took to solve....
Manager
Joined: 15 Jul 2008
Posts: 205

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08 Aug 2008, 05:28
arjtryarjtry wrote:
The geometric series a+ar+ar^2............. has a sum of 7, and the terms involving odd powers of r have a sum of 3. What is a+r?

4/3
12/7
3/2
7/3
5/2

mention how long it took to solve....

5/2 is the ans i got.

It is a geometric sequence. Convergence is given (7&3) and so the formula, Sn = a/(1-r) where a is the first term and r is the ratio between consecutive terms, can be used. Also because the series converges, r <1.

a/(1-r) = 7 ...... (1)

Sum of all odd powered r terms is 3. So ar is ur first term and r^2 is the ration between two consec terms.
ar/(1-r^2) = 3.....(2)

divide (1) by (2)

(r+1)/r = 7/3 solve to get r=3/4. Plug into (1) to get a=7/4

r+a = 10/4 = 5/2

Last edited by bhushangiri on 08 Aug 2008, 07:10, edited 2 times in total.
Director
Joined: 10 Sep 2007
Posts: 923

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08 Aug 2008, 05:31
Concept: Sum of infinite GP series = a/(1-r)

(Sum of whole series as given)
a/1-r = 7 => a = 7(1-r)....(1)

(Sum of odd numbers only, here r will be r^2)
ar/1-r^2 = 3, => 7(1-r)*r/(1-r)(1+r) = 3 (After substitution for a from 1)
=> 7r = 3 + 3r
=> r = 3/4...(2)
Substituting value of r in 1.
a = 7/4

a+ r = 7/4 + 3/4 = 10/4 = 5/2

If you know the GP series, then you can do it with in a minute.
SVP
Joined: 30 Apr 2008
Posts: 1855
Location: Oklahoma City
Schools: Hard Knocks

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08 Aug 2008, 06:51
I got 3 sequencing / progression questions on my real GMAT and I just kind of guessed at them. I really wish I could have gotten them right, who knows what my Q47 could have actually been.

Can you help me out and break down these steps into an "Idiot's Guide..." format?
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Manager
Joined: 15 Jul 2008
Posts: 205

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08 Aug 2008, 07:06
jallenmorris wrote:
I got 3 sequencing / progression questions on my real GMAT and I just kind of guessed at them. I really wish I could have gotten them right, who knows what my Q47 could have actually been.

Can you help me out and break down these steps into an "Idiot's Guide..." format?

Sum of geometric series has the general expression [ a(r^n -1 ) ] / (r-1) or it can be written as [ a(1- r^n ) ] / ( 1-r)

when r<1 and n --> infinity, r^n ---> 0 . That is how we get the formula. a/(1-r). It applies only to special case where r<0 and n --> infinity. And only then the series converges.

For finite n, you will need to use the whole expression.

For the current problem, refer my previous post. I edited it to make it a little better than earlier.. its a step by step soln.
Re: good series problem   [#permalink] 08 Aug 2008, 07:06
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# The geometric series a+ar+ar^2............. has a sum of 7,

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