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Manager  Joined: 07 Feb 2010
Posts: 118
If S is the infinite sequence S1 = 6, S2 = 12, ..., Sn = Sn-  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 73% (02:22) correct 27% (02:44) wrong based on 516 sessions

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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
##### Most Helpful Expert Reply
Math Expert V
Joined: 02 Sep 2009
Posts: 57155
Re: s in infinite sequence  [#permalink]

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6
7
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 $$\frac{first \ term+last \ term}{2}*# \ of \ terms=\frac{s_{13}+s_{28}}{2}*16=\frac{78+168}{2}*16=1968$$.

Answer: D.
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Manager  Joined: 25 Aug 2010
Posts: 61
Re: s in infinite sequence  [#permalink]

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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
Re: s in infinite sequence  [#permalink]

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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: 123
Re: s in infinite sequence  [#permalink]

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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: 20 Apr 2010
Posts: 174
Schools: ISB, HEC, Said
Re: s in infinite sequence  [#permalink]

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1
are we supposed to know this formula for GMAT?
Intern  Status: Current Student
Joined: 16 May 2010
Posts: 43
Schools: Darden '13
Sequence  [#permalink]

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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 D
Joined: 16 Oct 2010
Posts: 9541
Location: Pune, India
Re: Sequence  [#permalink]

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2
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 = $$\frac{28*29}{2} - \frac{12*13}{2} = 1968$$
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Manager  Joined: 30 Sep 2010
Posts: 51
Re: Sequence  [#permalink]

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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 D
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Re: s in infinite sequence  [#permalink]

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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.
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Schools: Ross '14 (M$) Re: s in infinite sequence [#permalink] ### Show Tags 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 Retired Moderator B Joined: 16 Nov 2010 Posts: 1347 Location: United States (IN) Concentration: Strategy, Technology Re: s in infinite sequence [#permalink] ### Show Tags (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 Answer - D _________________ 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: 6 Re: s in infinite sequence [#permalink] ### Show Tags 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 I do not know where I am making mistake. Can some one please help me.... Math Expert V Joined: 02 Sep 2009 Posts: 57155 Re: s in infinite sequence [#permalink] ### Show Tags 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 I do not know where I am making mistake. Can some one please help me.... 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. _________________ Manager  B Joined: 23 Dec 2013 Posts: 141 Location: United States (CA) GMAT 1: 710 Q45 V41 GMAT 2: 760 Q49 V44 GPA: 3.76 Re: If S is the infinite sequence S1 = 6, S2 = 12, ..., Sn = Sn- [#permalink] ### Show Tags 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 Sn = 6*N S13 = 6*13 S28 = 6*28 # of terms = 28 -13 + 1 = 16 (6*13+6*28)/2 = 3*(13+28) = 3*41 = 123 Once we have the mean of the set, we can multiply it by the number of terms in the set to arrive at the sum of those terms. 123*16 = 1968 EMPOWERgmat Instructor V Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 14824 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: If S is the infinite sequence S1 = 6, S2 = 12, ..., Sn = Sn- [#permalink] ### Show Tags Hi All, While many Test Takers will use a standard, algebraic approach to this question, you can also answer this question by using "bunching"…. Since we're dealing with the 13th through 28th terms, we're dealing with 16 terms…. The sum of the 1st and 16th term = 78 + 168 = 246 The sum of the 2nd and 15th term = 84 + 162 = 246 etc. So, we have 8 "sets" of 2 terms that all sum to 246 8(246) = 1968 If you calculate JUST the unit's digit, you'll have the correct answer (since only one answer has a units digit of 8). Final Answer: GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com *****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***** # Rich Cohen Co-Founder & GMAT Assassin Follow Special Offer: Save$75 + GMAT Club Tests Free
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Re: If S is the infinite sequence S1 = 6, S2 = 12, ..., Sn = Sn-  [#permalink]

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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

We see that the sequence is:

6, 12, 18, 24, …

This is an arithmetic sequence with first term S1 = 6 and common difference d = 6.

Recall that S_n = S1 + d(n - 1), so S13 = 6 + 6(13 - 1) = 78 and S28 = 6 + 6(28 - 1) = 168. To find the sum of a list of consecutive terms of an arithmetic sequence, we can use the formula:

(number of terms) x (first term + last term)/2

Here, the number of terms = 28 - 13 + 1 = 16, the first term = S13 = 78, and the last term = S28 = 168; thus; the sum of the terms form S13 to S28, inclusive, is:

16 x (78 + 168)/2

16 x 123

1,968

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

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1
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

$$S13 = 6* (13-1) + 6 = 78$$
$$S28 = 6* (28-1) + 6 = 168$$

Average of evenly spaced $$= \frac{First + Last}{2} = \frac{78 + 168}{2} = \frac{246}{2} = 123$$

Number of terms = Last - first + 1 = 28 - 13 + 1 = 15 + 1 = 16

16 * 123 = 1,968

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

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I went about it a different way. Given that each sequence is a multiple of 6 and we are doing addition, I focused on the pattern of repeated units,

S1 = 6 S26 = 6
S2 = 12 S27 = 2
S3 = 18 S28 = 8
S4 = 24
S5 = 30
S6 = 36

So a pattern of 5, then I just went through 28, of course not one by one, I started recounting at what S26 unit digit would be until I got to S28.

I only did this approach since I noticed the answer choices had different unit digits.
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If S is the infinite sequence S1 = 6, S2 = 12, ..., Sn = Sn-  [#permalink]

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Bunuel wrote:
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

Hello!

COuld someone please clarify to me how do we get to the following?

$$s_1+6(n-1)$$

Kind regards! If S is the infinite sequence S1 = 6, S2 = 12, ..., Sn = Sn-   [#permalink] 23 Jan 2019, 18:18

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

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