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# The infinite sequence a1, a2, , an, is such that a1 = 2, a2

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Senior Manager
Joined: 02 Dec 2007
Posts: 433
The infinite sequence a1, a2, , an, is such that a1 = 2, a2 [#permalink]

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20 Sep 2008, 07:26
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$$The infinite sequence a1, a2,…, an,… is such that a1 = 2, a2 = -3, a3 = 5, a4 = -1, and [m]an = an-4$$ for n > 4. What is the sum of the first 97 terms of the sequence[/m]?

A. 72
B. 74
C. 75
D. 78
E. 80

Last edited by Nihit on 20 Sep 2008, 07:59, edited 2 times in total.
VP
Joined: 21 Jul 2006
Posts: 1498

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20 Sep 2008, 07:48
Nihit wrote:
The infinite sequence a1, a2,…, an,… is such that a1 = 2, a2 = -3, a3 = 5, a4 = -1, and an = an-4 for n > 4. What is the sum of the first 97 terms of the sequence?

A. 72
B. 74
C. 75
D. 78
E. 80

question, is an= an-4 suppose to be an = a(n-4)?

because what you wrote up there doesn't make sense to me.
Director
Joined: 14 Aug 2007
Posts: 704

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20 Sep 2008, 07:52
the sum of first 4 terms is 3
terms will be repeated at interval of 4

there are 97/4= 24 such repeatations and then 97th term will be same as a1 = 2

the sum of first 97 terms will be 24*3 + 2 = 74

B
VP
Joined: 30 Jun 2008
Posts: 1022

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20 Sep 2008, 08:42
alpha_plus_gamma wrote:
terms will be repeated at interval of 4

alpha how did you deduce this ?

Thanks
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Joined: 05 Jul 2008
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20 Sep 2008, 18:04
1
KUDOS
amitdgr wrote:
alpha_plus_gamma wrote:
terms will be repeated at interval of 4

alpha how did you deduce this ?

Thanks

a 1=2, a 2= -3, a3 = 5 a4 =-1

an = an-4 means a5 =a1 a6 =a2 a7=a3 a8= a4 and so on

The first 97 would be

a1 + a2 +a3 + a4 + a5 + .... + a97 = 24 (a1+a2+a3+a4) + a97 which is 24 X 3 + 2 = 74

HTH
Re: sequence   [#permalink] 20 Sep 2008, 18:04
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# The infinite sequence a1, a2, , an, is such that a1 = 2, a2

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