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

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Manager
Joined: 08 Apr 2004
Posts: 131
Location: Corea
The infinite sequence a1, a2,, an, is such that a1 = 2, a2 = [#permalink]

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02 Sep 2004, 16:35
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The infinite sequence a1, a2,â€¦, an,â€¦ 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
Manager
Joined: 02 Apr 2004
Posts: 222
Location: Utrecht

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03 Sep 2004, 05:11
Somebody needs to explain this question to me please.

I am trying to look for an logical secuence:
A1 = 1 + 1 = 2
A2 = 2 - 5 = -3
A3 = 3 + 2
A4 = 4 - 5 = -1

A5 = 5 + 2 - 4 = 3
A6 = 6 - 5 - 4 = - 3
etc.

But what will be an fast calculation to add them all up?

Regards,

Alex
Intern
Joined: 27 Jul 2004
Posts: 27

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03 Sep 2004, 07:02
It stated "an=an-4", which means the Nth number equals the (N-4)th when N>4. So a5=a1, a6=a2 ...........

So
a1=2
a2=-3
a3=5
a4=-1

a5=2
a2=-3
a3=5
a4=-1
.
.
.
.
03 Sep 2004, 07:02
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