Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 24 May 2017, 11:59

### 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

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

# 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

Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 16 Feb 2011
Posts: 259
Followers: 4

Kudos [?]: 162 [0], given: 9

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

### Show Tags

15 Aug 2011, 02:39
1
This post was
BOOKMARKED
00:00

Difficulty:

(N/A)

Question Stats:

67% (02:15) correct 33% (01:17) wrong based on 48 sessions

### HideShow 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
Manager
Joined: 04 Jun 2011
Posts: 185
Followers: 0

Kudos [?]: 52 [1] , given: 21

Re: Sequence is making me go bonkers!! [#permalink]

### Show Tags

15 Aug 2011, 03:22
1
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
Intern
Joined: 02 Aug 2011
Posts: 9
Followers: 0

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

Re: Sequence is making me go bonkers!! [#permalink]

### Show Tags

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?
Math Forum Moderator
Joined: 20 Dec 2010
Posts: 2013
Followers: 163

Kudos [?]: 1822 [1] , given: 376

Re: Sequence is making me go bonkers!! [#permalink]

### Show Tags

15 Aug 2011, 04:46
1
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"
_________________
Manager
Joined: 04 Jun 2011
Posts: 185
Followers: 0

Kudos [?]: 52 [1] , given: 21

Re: Sequence is making me go bonkers!! [#permalink]

### Show Tags

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.
Manager
Joined: 04 Jun 2011
Posts: 185
Followers: 0

Kudos [?]: 52 [0], given: 21

Re: Sequence is making me go bonkers!! [#permalink]

### Show Tags

15 Aug 2011, 05:02
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!!
Current Student
Status: Everyone is a leader. Just stop listening to others.
Joined: 22 Mar 2013
Posts: 960
Location: India
GPA: 3.51
WE: Information Technology (Computer Software)
Followers: 171

Kudos [?]: 1611 [0], given: 229

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

### Show Tags

08 Sep 2014, 00:21
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
_________________

Piyush K
-----------------------
Our greatest weakness lies in giving up. The most certain way to succeed is to try just one more time. ― Thomas A. Edison
Don't forget to press--> Kudos
My Articles: 1. WOULD: when to use? | 2. All GMATPrep RCs (New)
Tip: Before exam a week earlier don't forget to exhaust all gmatprep problems specially for "sentence correction".

If S(n) is the sum of sequence 1, 2, 3, 4, ...n, in terms of   [#permalink] 08 Sep 2014, 00:21
Similar topics Replies Last post
Similar
Topics:
5 The sequence of s1, s2, s3, . . . , sn of n is such that sk = 2k -1 if 5 17 Mar 2017, 09:20
43 The sequence s1, s2, s3, ..., sn, ... is such that Sn=1/n- 9 16 Jul 2016, 03:52
7 The sequence s1, s2, s3,.....sn,...is such that Sn= 3 26 Apr 2012, 07:57
2 The sequence S1, S2, S3..., Sn ... is such that Sn= 1/n - 1/(n+1). If 4 25 Nov 2016, 23:19
63 The sequence s1, s2, s3,.....sn,...is such that Sn= (1/n) - 23 18 Oct 2016, 02:00
Display posts from previous: Sort by