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If S is the infinite sequence S1 = 6, S2 = 12, ..., Sn = [#permalink]
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15 Feb 2008, 14:34
This topic is locked. If you want to discuss this question please repost it in the respective forum. If S is the infinite sequence S1 = 6, S2 = 12, ..., Sn = Sn1 + 6,..., what is the sum of all terms in the set {S13, S14, ..., S28}? 1,800 1,845 1,890 1,968 2,016
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Re: MGMAT  Sequence [#permalink]
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15 Feb 2008, 14:57
bmwhype2 wrote: If S is the infinite sequence S1 = 6, S2 = 12, ..., Sn = Sn1 + 6,..., what is the sum of all terms in the set {S13, S14, ..., S28}? 1,800 1,845 1,890 1,968 2,016 sum = ((s13+s28)/2)*(2813+1) = (s13+s28)*8 = (6 + 12*6+6+27*6)*8 = 6*8*(2+27+12)=6*8*41 = 1968 > D



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Re: MGMAT  Sequence [#permalink]
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15 Feb 2008, 19:32
i started going this way, but got stuck .. i must be missing something basic.
Sn=6*n ... so S1=6, S2=12 and so on.
Sum of terms from S13 to S28 can be written as : 6*(13+14+...+28). Now, where can I go from here ?
edit: oops, just got it. I think theres a formula you use for sum of consecutive terms...
(last term + first term)/2 * (number of terms in sequence)
What cases does this formula apply in ?



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Re: MGMAT  Sequence [#permalink]
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16 Feb 2008, 00:39
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bmwhype2 wrote: If S is the infinite sequence S1 = 6, S2 = 12, ..., Sn = Sn1 + 6,..., what is the sum of all terms in the set {S13, S14, ..., S28}? 1,800 1,845 1,890 1,968 2,016 Basically its just (n1)*6+6 so S13 is (12)6+6 > 78 S28 is (27)6+6 > 168 Now there are 16 terms from 13 to 28 and the average is (168+78)/2 > Now just 16*123 > 1968 D



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Re: MGMAT  Sequence [#permalink]
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16 Feb 2008, 10:40
Basically need to realize that each increment will be times 6.
For example
The set starting at 1 is: x, 2x, 3x, 4x, 5x... where x = 6.
So we need to sum 13x > 28x. We just use the summation formula:
(16/2) * 41 = 328x = 328(6) = 1968 D.



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Re: MGMAT  Sequence [#permalink]
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17 Feb 2008, 12:33
+1 to GMATBLACKBELT....really simple less than 2min approach....
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Re: MGMAT  Sequence [#permalink]
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19 Feb 2008, 08:36
GMATBLACKBELT wrote: bmwhype2 wrote: If S is the infinite sequence S1 = 6, S2 = 12, ..., Sn = Sn1 + 6,..., what is the sum of all terms in the set {S13, S14, ..., S28}? 1,800 1,845 1,890 1,968 2,016 Basically its just (n1)*6+6 so S13 is (12)6+6 > 78 S28 is (27)6+6 > 168 Now there are 16 terms from 13 to 28 and the average is (168+78)/2 > Now just 16*123 > 1968 D thanks. this is why i post questions that i know. i did the entire problem via AP and then sum of AP, it took 3 minutes to solve.
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Re: MGMAT  Sequence [#permalink]
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20 Feb 2008, 01:27
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I did it in 60 seconds. Here's my way Rewrite Sn as S(n) = 6*n. So we want 6(13) + 6(14) + ... + 6(28) = 6 (13 + 14 + ... + 28 ) = 6 ( sum of first 28 numbers  sum of first 12 numbers ) = 6 ( 28*29/2  12*13 / 2 ) = 3 ( 812  156 ) = 3 ( 656 ) = 1968 D) Good question




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