It is currently 24 Sep 2017, 18:09

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

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

  post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
Current Student
User avatar
Joined: 11 May 2008
Posts: 555

Kudos [?]: 216 [0], given: 0

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

Show Tags

New post 08 Aug 2008, 04:47
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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....

Kudos [?]: 216 [0], given: 0

Manager
Manager
avatar
Joined: 15 Jul 2008
Posts: 206

Kudos [?]: 66 [0], given: 0

Re: good series problem [#permalink]

Show Tags

New post 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.

Kudos [?]: 66 [0], given: 0

Director
Director
avatar
Joined: 10 Sep 2007
Posts: 936

Kudos [?]: 327 [0], given: 0

Re: good series problem [#permalink]

Show Tags

New post 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.

Kudos [?]: 327 [0], given: 0

SVP
SVP
User avatar
Joined: 30 Apr 2008
Posts: 1870

Kudos [?]: 607 [0], given: 32

Location: Oklahoma City
Schools: Hard Knocks
Re: good series problem [#permalink]

Show Tags

New post 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?
_________________

------------------------------------
J Allen Morris
**I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$.

GMAT Club Premium Membership - big benefits and savings

Kudos [?]: 607 [0], given: 32

Manager
Manager
avatar
Joined: 15 Jul 2008
Posts: 206

Kudos [?]: 66 [0], given: 0

Re: good series problem [#permalink]

Show Tags

New post 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.

Kudos [?]: 66 [0], given: 0

Re: good series problem   [#permalink] 08 Aug 2008, 07:06
Display posts from previous: Sort by

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

  post reply Question banks Downloads My Bookmarks Reviews Important topics  


cron

GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.