If S is the infinite sequence S1 = 6, S2 = 12, ..., Sn = Sn- : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 17 Jan 2017, 00:59

### 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 is the infinite sequence S1 = 6, S2 = 12, ..., Sn = Sn-

Author Message
TAGS:

### Hide Tags

Manager
Joined: 07 Feb 2010
Posts: 159
Followers: 2

Kudos [?]: 551 [1] , given: 101

If S is the infinite sequence S1 = 6, S2 = 12, ..., Sn = Sn- [#permalink]

### Show Tags

04 Oct 2010, 06:17
1
KUDOS
2
This post was
BOOKMARKED
00:00

Difficulty:

25% (medium)

Question Stats:

74% (02:51) correct 26% (02:00) wrong based on 271 sessions

### HideShow timer Statistics

If S is the infinite sequence S1 = 6, S2 = 12, ..., Sn = Sn-1 + 6, ..., what is the sum of all terms in the set {S13, S14, ..., S28}?

A. 1,800
B. 1,845
C. 1,890
D. 1,968
E. 2,016
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 36530
Followers: 7068

Kudos [?]: 92946 [4] , given: 10541

Re: s in infinite sequence [#permalink]

### Show Tags

04 Oct 2010, 06:51
4
KUDOS
Expert's post
5
This post was
BOOKMARKED
anilnandyala wrote:
If S is the infinite sequence S1 = 6, S2 = 12, ..., Sn = Sn-1 + 6,..., what is the sum of all terms in the set {S13, S14, ..., S28}?

a) 1,800

b) 1,845

c) 1,890

d) 1,968

e) 2,016

Given: $$s_1=6$$ and $$s_n=s_{n-1}+6=s_1+6(n-1)$$.

Question: sum of 16 elements from this sequence $$s_{13}+s_{14}+...+s_{28}=?$$

As $$s_n=s_1+6(n-1)$$ then $$s_{13}=6+6(13-1)=78$$ and $$s_{28}=6+6(28-1)=168$$.

Sum of 16 evenly spaced terms would be $$\frac{first \ term+last \ term}{2}*# \ of \ terms=\frac{s_{13}+s_{28}}{2}*16=\frac{78+168}{2}*16=1968$$.

_________________
Manager
Joined: 25 Aug 2010
Posts: 98
Followers: 1

Kudos [?]: 4 [0], given: 1

Re: s in infinite sequence [#permalink]

### Show Tags

04 Oct 2010, 10:50
S1 = 6, S2 = 12, ..., Sn = Sn-1 + 6,..., what is the sum of all terms in the set {S13, S14, ..., S28}?

formula = n/2(firstterm + last term)

= s13 to s28 ---> we have 16 terms so n will be = 16
first term = s13 = since term is getting added 6 to the next term, the 13th term will be = 13*6 = 78
s28 = 28*6 = 168

so the sum = n/2(first term + last term) = = > 16/2(78+168) ====> 1968
Intern
Joined: 24 Aug 2010
Posts: 5
Followers: 0

Kudos [?]: 4 [0], given: 0

Re: s in infinite sequence [#permalink]

### Show Tags

04 Oct 2010, 11:38
Sn = 6*n...
S1 = 6 * 1; S2 = 6*2; ...

From S13 to S28: 6*13 + 6*14 + ... + 6*28 = 6* (13 + 14 + ... + 28)

13 + 14 + ...= 16 * (13+28)/2 = 328

Therefore 6 * 328 = 1968 (only term that ends with 8)
Manager
Joined: 22 Aug 2008
Posts: 186
Followers: 5

Kudos [?]: 87 [0], given: 11

Re: s in infinite sequence [#permalink]

### Show Tags

04 Oct 2010, 16:49
s1=6, s2=12.
so s13=13*6 and s28=28*6
so the sum = number of terms*(first term + last term)/2
= 16*6*(13+28)/2
=1968
Manager
Joined: 19 Apr 2010
Posts: 210
Schools: ISB, HEC, Said
Followers: 4

Kudos [?]: 77 [1] , given: 28

Re: s in infinite sequence [#permalink]

### Show Tags

06 Oct 2010, 04:17
1
KUDOS
are we supposed to know this formula for GMAT?
Intern
Status: Current Student
Joined: 16 May 2010
Posts: 44
Schools: Darden '13
Followers: 0

Kudos [?]: 9 [0], given: 4

### Show Tags

13 Nov 2010, 16:59
This question comes from Manhattan GMAT. I don't understand how you find the rule for this sequence. I just used the "$$S_n$$=$$S_(n-1)$$+6" to try to find the numbers in the sequence, but I was wrong. It's 6n. Once I see that that is the answer in the solution I can see it, but how can I arrive to that on my own?

If S is the infinite sequence $$S_1$$ = 6, $$S_2$$ = 12, ..., $$S_n$$ = $$S_(n-1)$$ + 6,..., what is the sum of all terms in the set {$$S_13$$, $$S_14$$, ..., $$S_28$$}?
a) 1,800
b) 1,845
c) 1,890
d) 1,968
e) 2,016
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7119
Location: Pune, India
Followers: 2129

Kudos [?]: 13627 [2] , given: 222

### Show Tags

13 Nov 2010, 17:59
2
KUDOS
Expert's post
MateoLibre wrote:
This question comes from Manhattan GMAT. I don't understand how you find the rule for this sequence. I just used the "$$S_n$$=$$S_(n-1)$$+6" to try to find the numbers in the sequence, but I was wrong. It's 6n. Once I see that that is the answer in the solution I can see it, but how can I arrive to that on my own?

If S is the infinite sequence $$S_1$$ = 6, $$S_2$$ = 12, ..., $$S_n$$ = $$S_(n-1)$$ + 6,..., what is the sum of all terms in the set {$$S_{13}$$, $$S_{14}$$, ..., $$S_{28}$$}?
a) 1,800
b) 1,845
c) 1,890
d) 1,968
e) 2,016

This is an arithmetic progression: 6, 12, 18, 24, 30...... (or I can say it is the multiplication table of 6)
When they say S(n) = S(n - 1) + 6, they are giving you that every subsequent term is 6 more but just writing down the first few numbers you will realize that it is just the table of 6. This happens because the first term is 6 so every time you add 6, it just becomes the next number in the multiplication table of 6. How will you learn to observe such things? Just by practice!

First term - 6
Second term - 6x2
Third term - 6x3 and so on
so 13th term will be 6x13
14th term will be 6x14
.
.
28th term will be 6x28
I need to add 6x13 + 6x14 +....6x28 = 6(13 + 14 + ...28)
13 + 14 +..28 = Sum of first 28 terms - Sum of first 12 terms = $$\frac{28*29}{2} - \frac{12*13}{2} = 1968$$
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Manager Joined: 30 Sep 2010 Posts: 59 Followers: 1 Kudos [?]: 47 [0], given: 0 Re: Sequence [#permalink] ### Show Tags 13 Nov 2010, 21:25 need to add 6x13 + 6x14 +....6x28 = 6(13 + 14 + ...28) so 6 * (13+28)/2 * 16 = 3 * 41 * 16 = 1968 (sum of an arithmatic sequence = (first term + last term)/2 * no of terms) Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7119 Location: Pune, India Followers: 2129 Kudos [?]: 13627 [0], given: 222 Re: s in infinite sequence [#permalink] ### Show Tags 14 Nov 2010, 03:26 prashantbacchewar wrote: are we supposed to know this formula for GMAT? The formula is simply the formula of the sum of an AP. If a is the first term, d is the common difference, and n is the number of terms, then $$S = \frac{n}{2}(2a + (n-1)d)$$ or $$S = \frac{n}{2}(a + b)$$ b is the last term of the progression which is written as a + (n-1)d. The logic behind it is that take the average of the AP which is (a + b)/2 and multiply it by n, the number of terms as if the average in added n times rather than individual numbers. It makes complete sense. Look at the example: AP with 3 terms: 4 7 10 7 is the average. 4 is 3 less than 7 and 10 is 3 more. Rather than adding 4 and 10 to 7, I can add 7 two more times and still get the same answer. Since GMAT does not focus on formulas, generally you can solve the question in other ways too (like I have done in my solution). Of course some basic formulas you should be good with and Sum of n consecutive terms starting from 1 = n(n + 1)/2 is one of them. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

Veritas Prep Reviews

Senior Manager
Status: Happy to join ROSS!
Joined: 29 Sep 2010
Posts: 278
Concentration: General Management, Strategy
Schools: Ross '14 (M)
Followers: 20

Kudos [?]: 124 [0], given: 48

Re: s in infinite sequence [#permalink]

### Show Tags

25 Mar 2011, 03:40
There is a much easier way to deal with this problem.
a)13th member is equal to 13*6 = smth8 (ok, 78, but 7 does not matter)
b) how many members are there between 28th and 14th members (i.e how many members will we add to 13th member?) = (28-14)+1 = 15 member.
c) 15*6 = smth0 That is important: the sum of members 14th-28th will has the unit digit ZERO!
d) now... smth8+smth0 = smth8 or answer D in that case
SVP
Joined: 16 Nov 2010
Posts: 1672
Location: United States (IN)
Concentration: Strategy, Technology
Followers: 33

Kudos [?]: 514 [0], given: 36

Re: s in infinite sequence [#permalink]

### Show Tags

27 Mar 2011, 00:39
(2)^1/3, (5)^1/6, (10)^1/10, (30)^1/15

s13 = s1 + (12) * 6

=> s13 = 13 * 6 = 78

s28 = s1 + 27 * 6

s28 = 28 * 6 = 168

So Sum = 16 * (78 + 168)/2

= 8 * 246

The answer must end with last digit as 8 and We can stop multiplying here as there is only 1 answer like that.

= 1968

_________________

Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

GMAT Club Premium Membership - big benefits and savings

Intern
Joined: 22 Apr 2010
Posts: 7
Followers: 0

Kudos [?]: 6 [0], given: 2

Re: s in infinite sequence [#permalink]

### Show Tags

15 Feb 2012, 05:50
Can we solve the below sum using this approach

S13-S28 = {S1-S28} - {S1-S13}

S1-S28 = n/2 {2a+(n-1)d} =28/2 { 2*6 + 27*6} = 2436
S1-S13 = n/2{2a+(n-1)d} = 13/2{2*6+12 *6} = 546

S13-S28 =2436-546 =1890

Math Expert
Joined: 02 Sep 2009
Posts: 36530
Followers: 7068

Kudos [?]: 92946 [0], given: 10541

Re: s in infinite sequence [#permalink]

### Show Tags

15 Feb 2012, 10:19
prakarp wrote:
Can we solve the below sum using this approach

S13-S28 = {S1-S28} - {S1-S13}

S1-S28 = n/2 {2a+(n-1)d} =28/2 { 2*6 + 27*6} = 2436
S1-S13 = n/2{2a+(n-1)d} = 13/2{2*6+12 *6} = 546

S13-S28 =2436-546 =1890

The sum of all terms in the set {S13, S14, ..., S28} means the sum of all the terms from S13 to S28, inclusive. So, it equals to the sum of first 28 terms minus the sum of first 12 terms;

Hence it should be: the sum of first 28 terms minus the sum of first 12 terms = 2436-468=1968.

Hope it's clear.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13421
Followers: 575

Kudos [?]: 163 [0], given: 0

Re: If S is the infinite sequence S1 = 6, S2 = 12, ..., Sn = Sn- [#permalink]

### Show Tags

30 Sep 2013, 04:03
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13421
Followers: 575

Kudos [?]: 163 [0], given: 0

Re: If S is the infinite sequence S1 = 6, S2 = 12, ..., Sn = Sn- [#permalink]

### Show Tags

24 Oct 2014, 07:36
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13421
Followers: 575

Kudos [?]: 163 [0], given: 0

Re: If S is the infinite sequence S1 = 6, S2 = 12, ..., Sn = Sn- [#permalink]

### Show Tags

01 Jun 2016, 10:44
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: If S is the infinite sequence S1 = 6, S2 = 12, ..., Sn = Sn-   [#permalink] 01 Jun 2016, 10:44
Similar topics Replies Last post
Similar
Topics:
10 A certain sequence is defined by the following rule: Sn = k(Sn–1), whe 5 12 Jun 2015, 02:10
10 Sn = n^2 + 5n + 94 and K = S6 – S5 + S4 – S3 + S2 – S1. What is the 5 11 Jun 2015, 03:33
4 The sequence S is defined as Sn = (n + 1)! 4 27 Dec 2014, 15:29
5 Sequence S is defined as follows: S1=2, S2=2^1, S3=2^2, SN=2 3 21 Mar 2012, 04:18
30 S is the infinite sequence S1=2, S2=22, S3=222 22 18 Jul 2010, 14:47
Display posts from previous: Sort by