The infinite sequence a(1), a(2),, a(n), is such that a(1) = : PS Archive
Check GMAT Club App Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

It is currently 07 Dec 2016, 10:25
GMAT Club Tests

Admission

Help Desk is Open: Join Chat Room1 to Discuss your Queries with MBA Expert |  Join Chat Room2 for Chicago-Booth Decision Updates


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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

The infinite sequence a(1), a(2),, a(n), is such that a(1) =

  post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
VP
VP
User avatar
Joined: 09 Jul 2007
Posts: 1104
Location: London
Followers: 6

Kudos [?]: 101 [0], given: 0

The infinite sequence a(1), a(2),, a(n), is such that a(1) = [#permalink]

Show Tags

New post 10 Dec 2007, 15:08
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions

HideShow timer Statistics

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

The infinite sequence a(1), a(2),…, a(n),… is such that a(1) = 2, a(2) = -3, a(3) = 5, a(4) = -1, and a(n) = a(n-4) for n > 4. What is the sum of the first 97 terms of the sequence?

A. 72
B. 74
C. 75
D. 78
E. 80


B
Expert Post
CEO
CEO
User avatar
Joined: 17 Nov 2007
Posts: 3589
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 530

Kudos [?]: 3455 [0], given: 360

 [#permalink]

Show Tags

New post 10 Dec 2007, 15:15
B.

a(97)=a(4*24+1)

∑a(1..97)=24*∑a(1..4)+a(97)=24*3+a(1)=72+2=74
VP
VP
User avatar
Joined: 09 Jul 2007
Posts: 1104
Location: London
Followers: 6

Kudos [?]: 101 [0], given: 0

 [#permalink]

Show Tags

New post 10 Dec 2007, 19:07
thanks walker. no other simpler methods??
Director
Director
User avatar
Joined: 12 Jul 2007
Posts: 862
Followers: 15

Kudos [?]: 280 [0], given: 0

 [#permalink]

Show Tags

New post 10 Dec 2007, 19:33
walker wrote:
B.

a(97)=a(4*24+1)

∑a(1..97)=24*∑a(1..4)+a(97)=24*3+a(1)=72+2=74


can you break this down step by step for me? thanks in advance
Director
Director
avatar
Joined: 09 Aug 2006
Posts: 763
Followers: 1

Kudos [?]: 189 [0], given: 0

Re: PS [#permalink]

Show Tags

New post 11 Dec 2007, 03:44
Ravshonbek wrote:
The infinite sequence a(1), a(2),…, a(n),… is such that a(1) = 2, a(2) = -3, a(3) = 5, a(4) = -1, and a(n) = a(n-4) for n > 4. What is the sum of the first 97 terms of the sequence?

A. 72
B. 74
C. 75
D. 78
E. 80


B


74.

a(5) = a(4)
a(6) = a(2) and so on.

So the series is basically the first 4 terms repeated 97 times:
2, -3 , 5, -1, 2, -3 , 5, -1, ... and so on.

Sum of the 1st 4 terms = 3
These same terms are repeated 97 = 96 + 1 times
Therefore, the sum will be 96/4*3 + 1st term = 72 + 2 = 74
Expert Post
CEO
CEO
User avatar
Joined: 17 Nov 2007
Posts: 3589
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 530

Kudos [?]: 3455 [0], given: 360

 [#permalink]

Show Tags

New post 11 Dec 2007, 03:55
eschn3am wrote:
can you break this down step by step for me? thanks in advance


1 a(n) = a(n-4) for n > 4: we have the sequence of numbers with period 4

2. for any M=4*k+r: a(M)=a(r)

3. we can transform ∑a(1..M) to:

∑a(1..M) = ∑a(1..4) + ∑a(5..8) + .... + ∑a(4*(k-1)+1..4*k)... + ∑a(1..r)

put ∑a(1..4) insead of ∑a(5..8) and ∑a(4*(k-1)+1..4*k))

∑a(1..M) = k*∑a(1..4)+ ∑a(1..r)

4. M=97=4*24+1 ==> ∑a(1..97) = 24*∑a(1..4)+ ∑a(1..1) = 24*3+a(1)=72+2=74
  [#permalink] 11 Dec 2007, 03:55
Display posts from previous: Sort by

The infinite sequence a(1), a(2),, a(n), is such that a(1) =

  post reply Question banks Downloads My Bookmarks Reviews Important topics  


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

Powered by phpBB © phpBB Group and phpBB SEO

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®.