Find all School-related info fast with the new School-Specific MBA Forum

It is currently 23 Jul 2014, 17:56

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If S(n) is the sum of sequence 1, 2, 3, 4, ...n, in terms of

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Senior Manager
Senior Manager
avatar
Joined: 15 Feb 2011
Posts: 263
Followers: 4

Kudos [?]: 12 [0], given: 9

GMAT Tests User
If S(n) is the sum of sequence 1, 2, 3, 4, ...n, in terms of [#permalink] New post 15 Aug 2011, 01:39
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

50% (02:12) correct 50% (01:30) wrong based on 13 sessions
If S(n) is the sum of sequence 1, 2, 3, 4, ...n, in terms of n and S(n), S(2n)=?
(A) 2*S(n)
(B) n*S(n)
(C) 2n*S(n)
(D) 2S(n)+n^2
(E) S(n)+2n^2

Pls help with the easiest explanation possible..thnx
1 KUDOS received
Manager
Manager
avatar
Joined: 04 Jun 2011
Posts: 194
Followers: 0

Kudos [?]: 31 [1] , given: 21

GMAT Tests User
Re: Sequence is making me go bonkers!! [#permalink] New post 15 Aug 2011, 02:22
1
This post received
KUDOS
DeeptiM wrote:
If S(n) is the sum of sequence 1, 2, 3, 4, ...n, in terms of n and S(n), S(2n)=?
(A) 2*S(n)
(B) n*S(n)
(C) 2n*S(n)
(D) 2S(n)+n^2
(E) S(n)+2n^2

Pls help with the easiest explanation possible..thnx



for starters u could use the substitution technique where n =2 ==> sn = 3

then s(2n) = s(4) = 10 only D satisfies


however if ur looking to solve it mathematically,
Sn = n(a1 + an)/2 since this is an AP with difference = 1 and starting term a = 1

we can rewrite an as a+ (n-1)d = 1 + (n-1)

Therefore Sn = n(1+ n)/2 or n+n^2 = 2Sn -- (1)

S(2n) similarly = 2n[1 + 2n] / 2 = n + 2n^2 = n + n^2 + n^2

we know from (1)

S(2n) = 2Sn + n^2 hence answer D
1 KUDOS received
Math Forum Moderator
avatar
Joined: 20 Dec 2010
Posts: 2049
Followers: 125

Kudos [?]: 874 [1] , given: 376

GMAT Tests User
Re: Sequence is making me go bonkers!! [#permalink] New post 15 Aug 2011, 03:46
1
This post received
KUDOS
DeeptiM wrote:
If S(n) is the sum of sequence 1, 2, 3, 4, ...n, in terms of n and S(n), S(2n)=?
(A) 2*S(n)
(B) n*S(n)
(C) 2n*S(n)
(D) 2S(n)+n^2
(E) S(n)+2n^2

Pls help with the easiest explanation possible..thnx


Let's see the pattern:

For n=5, the sequence will be {1,2,3,4,5}
S(n)=S(5)=1+2+3+4+5

2n=2*5=10, the sequence will be {1,2,3,4,5,6,7,8,9,10}
S(2n)=S(10)=1+2+3+4+5+6+7+8+9+10=1+2+3+4+5+(1+5)+(2+5)+(3+5)+(4+5)+(5+5)
(1+2+3+4+5)+(1+2+3+4+5)+(5+5+5+5+5)
S(5)+S(5)+5*5=S(5)+S(5)+5^2=2S(5)+5^2

Since, n=5
2S(5)+5^2=2S(n)+n^2

In general terms,
S(n)=1+2+3+4,...+n
S(2n)=1+2+3+4,...+n+(1+n)+(2+n)+(3+n)+(4+n),...+(n+n)
S(2n)=(1+2+3+4+...+n)+(1+2+3+4+...n)+(n+n+...n-times)
S(2n)=S(n)+S(n)+n^2
S(2n)=2S(n)+n^2

Ans: "D"
_________________

~fluke

Get the best GMAT Prep Resources with GMAT Club Premium Membership

1 KUDOS received
Manager
Manager
avatar
Joined: 04 Jun 2011
Posts: 194
Followers: 0

Kudos [?]: 31 [1] , given: 21

GMAT Tests User
Re: Sequence is making me go bonkers!! [#permalink] New post 15 Aug 2011, 03:59
1
This post received
KUDOS
meshell wrote:
"for starters u could use the substitution technique where n =2 ==> sn = 3

then s(2n) = s(4) = 10 only D satisfies"

Can you explain how you would get s(n) = 3 if n is 2. disregarding the format of the sequence, if n is 2, the sum of the sequence should be at least 12 (10...+ 2).

its clearly much quicker than doing it mathematically! but I did go the math route, and my only falter compared to your calculation is that I cannot see how you've got rid of the division by 2 in the S(n) calculations.

"Therefore Sn = n(1+ n)/2 or n+n^2 = 2Sn -- (1)"

Shouldn't n(1 + n) / 2 become n + n^2 / 2?




Michelle, the series is 1,2,3,4,....
and Sn is the sum of the series until n terms .. so the sum of the series for 2 terms or s(2) = 1+2 = 3

and s(4) = 1+2+3+4 = 10


i hope this helps explain your concern on "disregarding the format of the sequence, if n is 2, the sum of the sequence should be at least 12 (10...+ 2). "
if you still have questions, i'll be happy to help.

on the mathematical formula yes sn = [n(1+n)] / 2 and is therefore indeed sn = [n + n^2] / 2
but to avoid confusion, i have pulled the 2 to the other side making it 2* Sn = [n + n^2]

so (n + n^2 ) equals 2*Sn and not just Sn.
Intern
Intern
avatar
Joined: 02 Aug 2011
Posts: 10
Followers: 0

Kudos [?]: 1 [0], given: 1

Re: Sequence is making me go bonkers!! [#permalink] New post 15 Aug 2011, 03:27
"for starters u could use the substitution technique where n =2 ==> sn = 3

then s(2n) = s(4) = 10 only D satisfies"

Can you explain how you would get s(n) = 3 if n is 2. disregarding the format of the sequence, if n is 2, the sum of the sequence should be at least 12 (10...+ 2).

its clearly much quicker than doing it mathematically! but I did go the math route, and my only falter compared to your calculation is that I cannot see how you've got rid of the division by 2 in the S(n) calculations.

"Therefore Sn = n(1+ n)/2 or n+n^2 = 2Sn -- (1)"

Shouldn't n(1 + n) / 2 become n + n^2 / 2?
Manager
Manager
avatar
Joined: 04 Jun 2011
Posts: 194
Followers: 0

Kudos [?]: 31 [0], given: 21

GMAT Tests User
Re: Sequence is making me go bonkers!! [#permalink] New post 15 Aug 2011, 04:02
fluke wrote:
DeeptiM wrote:
If S(n) is the sum of sequence 1, 2, 3, 4, ...n, in terms of n and S(n), S(2n)=?
(A) 2*S(n)
(B) n*S(n)
(C) 2n*S(n)
(D) 2S(n)+n^2
(E) S(n)+2n^2

Pls help with the easiest explanation possible..thnx


Let's see the pattern:

For n=5, the sequence will be {1,2,3,4,5}
S(n)=S(5)=1+2+3+4+5

2n=2*5=10, the sequence will be {1,2,3,4,5,6,7,8,9,10}
S(2n)=S(10)=1+2+3+4+5+6+7+8+9+10=1+2+3+4+5+(1+5)+(2+5)+(3+5)+(4+5)+(5+5)
(1+2+3+4+5)+(1+2+3+4+5)+(5+5+5+5+5)
S(5)+S(5)+5*5=S(5)+S(5)+5^2=2S(5)+5^2

Since, n=5
2S(5)+5^2=2S(n)+n^2

In general terms,
S(n)=1+2+3+4,...+n
S(2n)=1+2+3+4,...+n+(1+n)+(2+n)+(3+n)+(4+n),...+(n+n)
S(2n)=(1+2+3+4+...+n)+(1+2+3+4+...n)+(n+n+...n-times)
S(2n)=S(n)+S(n)+n^2
S(2n)=2S(n)+n^2

Ans: "D"



Thanks Fluke for saving my back on so many occasions :-) kudos to u!!
Re: Sequence is making me go bonkers!!   [#permalink] 15 Aug 2011, 04:02
    Similar topics Author Replies Last post
Similar
Topics:
1 If Sn is the sum of the first n terms of a certain sequence MensaNumber 4 03 Jun 2014, 17:50
10 Experts publish their posts in the topic The sequence s1, s2, s3, ..., sn, ... is such that Sn=1/n- Bunuel 7 23 Feb 2014, 06:46
Experts publish their posts in the topic The sequence s1, s2, s3,.....sn,...is such that Sn= Stiv 3 26 Apr 2012, 06:14
14 Experts publish their posts in the topic The sequence s1, s2, s3,.....sn,...is such that Sn= (1/n) - metallicafan 19 17 Aug 2010, 11:46
Sequence 1, 2, 3, 4, ...an...In terms of n, S(2n)-S(n)? I az780 1 11 Mar 2008, 09:37
Display posts from previous: Sort by

If S(n) is the sum of sequence 1, 2, 3, 4, ...n, in terms of

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| 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®.