There is a sequence A(n) with positive integers in condition : PS Archive
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# There is a sequence A(n) with positive integers in condition

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11 Dec 2005, 05:37
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There is a sequence A(n) with positive integers in condition that A(n+2)=A(n+1)+A(n), when the sum of the preceding two A(i)s is even, is divided by 2 and, when the sum of the preceding two A(i)s is odd, is itself. A(5)=5, A(4)=7, what is the value of A(1) ?

A. 2 B. 3 C. 4 D. 5 E. 6
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11 Dec 2005, 08:04
2.

A(5)=5, A(4)=7

as A(5) < A(4), sum of A(4) and A(3) should be even

A(5) = {A(4) + A(3)} / 2

5 = (7 + A(3))/2

A(3) = 3

A(4) = A(3) + A(2)
7 = 3 + A(2)
A(2) = 4

A(3) = {A(2) + A(1)}/2
3 = {4 + A(1)}/2
A(1) = 2
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