NEW HERE? LEARN MORE
closeclose
It is currently 19 Apr 2024, 17:25
Register
GMAT Focus Tests
Decision Tracker
My Rewards
New posts
New comers' posts

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

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

16 posts Go to First Unread Post
Print view
NEW TOPIC
POST REPLY
Question banks

GMAT Question Banks

Downloads
My Bookmarks
Reviews
SORT BY:
Date
Kudos
User avatar
DeeptiM
Manager
Manager
Joined: 16 Feb 2011
Posts: 142
If S(n) is the sum of sequence 1, 2, 3, 4, ...n, in terms of [#permalink] New post  Updated on: 17 Aug 2017, 05:53
4
Kudos
62
Bookmarks
00:00
A
B
C
D
E

Difficulty:

45% (medium)

Question Stats:

67% (02:17) correct 33% (01:50) wrong based on 1197 sessions
Hide Show timer Statistics
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
ShowHide Answer
Official Answer
Official Answer and Stats are available only to registered users. Register/Login.

Originally posted by DeeptiM on 15 Aug 2011, 02:39.
Last edited by abhimahna on 17 Aug 2017, 05:53, edited 1 time in total.
Added OA.
Most Helpful Reply
User avatar
viks4gmat
Manager
Manager
Joined: 04 Jun 2011
Posts: 99
Re: If S(n) is the sum of sequence 1, 2, 3, 4, ...n, in terms of [#permalink] New post  15 Aug 2011, 03:22
6
Kudos
3
Bookmarks
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
User avatar
B
PiyushK
Director
Director
Joined: 22 Mar 2013
Status:Everyone is a leader. Just stop listening to others.
Posts: 611
Location: India
GPA: 3.51
WE:Information Technology (Computer Software)
Reviews Badge
Re: If S(n) is the sum of sequence 1, 2, 3, 4, ...n, in terms of [#permalink] New post  08 Sep 2014, 00:21
7
Kudos
W.K.T
\(S(n)=\frac{n(n+1)}{2}\) ---- first relation

\(S(2n)=\frac{2n(2n+1)}{2}\)

\(S(2n)=2n(\frac{n}{2}+\frac{n+1}{2})\)

\(Substitute \frac{n+1}{2} = \frac{S(n)}{n} --from-1st-relation\)

\(S(2n)=2n(\frac{n}{2}+\frac{S(n)}{n})\)

reduce

\(S(2n) = n^2 + 2S(n)\)

Ans : D
General Discussion
avatar
meshell
Intern
Intern
Joined: 02 Aug 2011
Posts: 6
Re: If S(n) is the sum of sequence 1, 2, 3, 4, ...n, in terms of [#permalink] New post  15 Aug 2011, 04:27
"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?
User avatar
fluke
Retired Moderator
Joined: 20 Dec 2010
Posts: 1114
Re: If S(n) is the sum of sequence 1, 2, 3, 4, ...n, in terms of [#permalink] New post  15 Aug 2011, 04:46
6
Kudos
1
Bookmarks
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"
User avatar
viks4gmat
Manager
Manager
Joined: 04 Jun 2011
Posts: 99
Re: If S(n) is the sum of sequence 1, 2, 3, 4, ...n, in terms of [#permalink] New post  15 Aug 2011, 04:59
1
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.
User avatar
viks4gmat
Manager
Manager
Joined: 04 Jun 2011
Posts: 99
Re: If S(n) is the sum of sequence 1, 2, 3, 4, ...n, in terms of [#permalink] New post  15 Aug 2011, 05:02
1
Bookmarks
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!!
avatar
S
AbhimanyuDhar
Intern
Intern
Joined: 14 Oct 2016
Posts: 31
Location: India
WE:Sales (Energy and Utilities)
Re: If S(n) is the sum of sequence 1, 2, 3, 4, ...n, in terms of [#permalink] New post  12 Sep 2017, 12:34
S(n)=n(n+1)/2

S(n)=(n/2 )(n+1)

S(2n)=(2n/2)(2n+1)

S(2n)=n(2n+1)
S(2n)=2n^2+n

S(2n)=(n^2)+n +(n^2)
S(2n)= 2S(n)+ n^2
avatar
S
AD2GMAT
Manager
Manager
Joined: 30 Jul 2014
Status:MBA Completed
Affiliations: IIM
Posts: 91
Reviews Badge
Re: If S(n) is the sum of sequence 1, 2, 3, 4, ...n, in terms of [#permalink] New post  14 Sep 2017, 01:01
I calculated 2*S(n) in place of S(2*n) - silly mistake, and hence landed up in the answer option A.
User avatar
P
Probus
Manager
Manager
Joined: 10 Apr 2018
Posts: 187
Location: United States (NC)
Re: If S(n) is the sum of sequence 1, 2, 3, 4, ...n, in terms of [#permalink] New post  13 Aug 2018, 07:23
3
Kudos
Hi,
If S(n) = n(n+1)/ 2
or n^2+n= 2S(n) ....... (i)
then S(2n)= 2n(2n+1)/2
= n(2n+1)
= 2n^2 +n
=n^2+n^2+n
= n^2 + 2S(n) { substituting the value from eq i)

Bunuel,
Can we move this to PS forum.
_________________
Probus

~You Just Can't beat the person who never gives up~ Babe Ruth
Signature Read More
User avatar
S
Izzyjolly
Intern
Intern
Joined: 06 Nov 2016
Posts: 49
Location: Viet Nam
Concentration: Strategy, International Business
GPA: 3.54
Re: If S(n) is the sum of sequence 1, 2, 3, 4, ...n, in terms of [#permalink] New post  13 Aug 2018, 10:18
3
Kudos
2
Bookmarks
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


1. Number plugging approach: Let n = 3, we have
S(n) = S(3) = 1+2+3 = 6
S(2n) = S(6) = 1+2+3+4+5+6 = 21
--> D is the answer.

2. Mathematical approach:
\(S(n) = 1+2+3+...+(n-1)+n = \frac{(n+1)*n}{2}\)
--> \((n+1)*n = 2* S(n)\)
\(S(2n) = 1+2+3+...+(2n-1)+2n = \frac{(2n+1)*2n}{2}\) = \((2n+1)*n\) = \((n+1)*n\) + \(n*n\) = \(2*S(n)\) + \(n^2\)
--> Answer D.

To moderators
This is a PS question. Please move it to PS subforum.
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92760
CAT Tests Forum Quiz Mode
Re: If S(n) is the sum of sequence 1, 2, 3, 4, ...n, in terms of [#permalink] New post  13 Aug 2018, 11:46
Expert Reply
Probus wrote:
Hi,
If S(n) = n(n+1)/ 2
or n^2+n= 2S(n) ....... (i)
then S(2n)= 2n(2n+1)/2
= n(2n+1)
= 2n^2 +n
=n^2+n^2+n
= n^2 + 2S(n) { substituting the value from eq i)

Bunuel,
Can we move this to PS forum.


_____________
Done. Thank you.
_________________
New to the GMAT CLUB Forum?

My Signature Questions' Collection:


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics
Signature Read More
User avatar
P
GyMrAT
Senior Manager
Senior Manager
Joined: 14 Dec 2017
Posts: 426
Location: India
Re: If S(n) is the sum of sequence 1, 2, 3, 4, ...n, in terms of [#permalink] New post  13 Aug 2018, 12:05
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


Given \(S(n) = 1 + 2 + 3 +.....+ n\)

\(S(2n) = 1 + 2 + 3 +......+ n + (n+1) + (n+2) +.......+ (n+n)\)

\(S(2n) - S(n) = (n+1) + (n+2) +.......+ (n+n) = n*n + (1 + 2 + 3 +....n)\)

hence \(S(2n) = n^2 + 2S(n)\)


Answer D.


Thanks,
GyM
_________________
New to GMAT Club - https://gmatclub.com/forum/new-to-gmat-club-need-help-271131.html#p2098335
Signature Read More
User avatar
G
KanishkM
Director
Director
Joined: 09 Mar 2018
Posts: 783
Location: India
Schools: DeGroote'21 Desautels '21 NUS '21
Re: If S(n) is the sum of sequence 1, 2, 3, 4, ...n, in terms of [#permalink] New post  13 Jan 2019, 13:12
2
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 this question, i just assumed a series of 5 numbers 1,2,3,4,5
S(n) = 15 and n = 5

S(2n) = 55 ( 1,2,3,4,5,6,7,8,9,10)

Now we need to find 55 when we substitute the values for n and S(n) in the answer options
(A) 2*S(n) => 2* 15 =30
(B) n*S(n) => 5*15 =75
(C) 2n*S(n) => 10*15 =150
(D) 2S(n)+n^2 => 55
(E) S(n)+2n^2

Answer D
_________________
Many of life's failures happen with people who do not realize how close they were to success when they gave up.
Signature Read More
User avatar
G
CEdward
VP
VP
Joined: 11 Aug 2020
Posts: 1263
Re: If S(n) is the sum of sequence 1, 2, 3, 4, ...n, in terms of [#permalink] New post  12 Apr 2021, 11:51
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"


Very tough problem because it takes a lot of time to see the pattern. Are there other questions like this?
_________________
"Do not pray for an easy life, pray for the strength to endure a difficult one." - Bruce Lee
Signature Read More
User avatar
S
Tiffsootmoot8
Manager
Manager
Joined: 23 Aug 2015
Posts: 53
Location: India
GPA: 2.99
Re: If S(n) is the sum of sequence 1, 2, 3, 4, ...n, in terms of [#permalink] New post  19 Aug 2023, 04:35
Keep it simple..
Substitute any value for n and calculate S(n) and S(2n)
For example, for n=4, S(4) = 10 and S(8) = 36.
Now try substituting n=4 for each of the options and see which one matches.
Only D works!
GMAT Club Bot
gmatclubot
Re: If S(n) is the sum of sequence 1, 2, 3, 4, ...n, in terms of [#permalink]
19 Aug 2023, 04:35
NEW TOPIC
POST REPLY
Downloads
My Bookmarks
Reviews
Moderators:
Bunuel
Math Expert
92760 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

cron

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions