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SEQUENCES

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SEQUENCES

by ajdjmba » Sun Jul 08, 2012 2:33 am
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}?

1,800
1,845
1,890
1,968
2,016

How to avoid lengthy process to solve this.
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Source: — Data Sufficiency |

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by Anurag@Gurome » Sun Jul 08, 2012 2:54 am
ajdjmba 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}?
S1 = 6 = 6*1
S2 = 12 = 6*2
S3 = 18 = 6*3
Hence, Sn = 6n

Therefore, (S13 + A14 + ... + S28) = (6*13 + 6*14 + ... + 6*28) = 6*(13 + 14 + ... + 28)

Now, from 13 to 28 there are 16 integers and their mean is (13 + 28)/2
Hence, (13 + 14 + ... + 28) = 16*(13 + 28)/2 = 8*41 = 328

Therefore, required sum = 6*328 = 1968

The correct answer is D.
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
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