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The infinite sequence a(1), a(2),, a(n), is such that a(1) = [#permalink]
10 Dec 2007, 15:08

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The infinite sequence a(1), a(2),…, a(n),… is such that a(1) = 2, a(2) = -3, a(3) = 5, a(4) = -1, and a(n) = a(n-4) for n > 4. What is the sum of the first 97 terms of the sequence?

The infinite sequence a(1), a(2),…, a(n),… is such that a(1) = 2, a(2) = -3, a(3) = 5, a(4) = -1, and a(n) = a(n-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

B

74.

a(5) = a(4)
a(6) = a(2) and so on.

So the series is basically the first 4 terms repeated 97 times:
2, -3 , 5, -1, 2, -3 , 5, -1, ... and so on.

Sum of the 1st 4 terms = 3
These same terms are repeated 97 = 96 + 1 times
Therefore, the sum will be 96/4*3 + 1st term = 72 + 2 = 74

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