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There is a sequence An for a positive integer n such that when An-2 is

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There is a sequence An for a positive integer n such that when An-2 is [#permalink]

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New post 19 Apr 2016, 06:02
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There is a sequence An for a positive integer n such that when An-2 is divided by An-1 the remainder is An. If A3=6, A4=0, which of the following can be the value of A1?
Attachment:
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A. 48
B. 50
C. 52
D. 56
E. 58


* A solution will be posted in two days.

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There is a sequence An for a positive integer n such that when An-2 is [#permalink]

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New post 19 Apr 2016, 07:54
When A1/A2, Remainder = A3 = 6 --> A1 = xA2 + 6

When A2/A3, Remainder = A4 = 0 --> A2 = yA3

A1 = xyA3 + 6 = kA3 + 6 = 6(k + 1) --> A1 must be a multiple of 6

Only option A is a multiple of 6

Answer: A
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Re: There is a sequence An for a positive integer n such that when An-2 is [#permalink]

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New post 19 Apr 2016, 15:43
1
An-2 =(An-1)Q + An

A2 = (A3)Q + A4

A2 = 6Q + 0 = 6Q

therefore
A1 = (6Q)Q + 6 = 6Q^2 + 6 = 6(Q^2 + 1)

Thus A1 is definitely divisible by 6
Out of the given options, only A is divisible by 6

Correct Option : A
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Re: There is a sequence An for a positive integer n such that when An-2 is [#permalink]

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New post 21 Apr 2016, 01:26
There is a sequence An for a positive integer n such that when An-2 is divided by An-1 the remainder is An. If A3=6, A4=0, which of the following can be the value of A1?

A. 48
B. 50
C. 52
D. 56
E. 58


==> If n=4, A2=A3Q+A4=6Q+0=6Q is derived.
If n=3, from A1=A2P+A3=6QP+6=6(QP+1), it becomes always a multiple of 6.
Thus, the answer is A.
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Re: There is a sequence An for a positive integer n such that when An-2 is [#permalink]

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New post 07 Oct 2017, 01:34
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Re: There is a sequence An for a positive integer n such that when An-2 is   [#permalink] 07 Oct 2017, 01:34
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