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There is a sequence An, such that A1=1，A2=2, and An+2=An+1+An+An1+….+ [#permalink]
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26 Jul 2017, 00:14
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There is a sequence An, such that A 1=1，A 2=2, and A n+2=A n+1+A n+A n1+….+A 2+A 1. What is the ratio of A 14 to A 11? A. 32 B. 16 C. 8 D. 4 E. 2
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There is a sequence An, such that A1=1，A2=2, and An+2=An+1+An+An1+….+ [#permalink]
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26 Jul 2017, 00:26
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We know that A n+2=A n+1+A n+A n1+….+A 2+A 1Given data: A 1=1 and A 2=2 From the above information, A 3 = A 1 + A 2 = 1 + 2 = 3 Similarly, A 4 = 3 + 2 + 1 = 6 The sequence will be 1,2,3,6,12,24,48,96,192,384,384*2,384*4,384*8,384*16. The ratio of A 14 to A 11 is \(\frac{384*16}{384*2}\) = 8(Option C)
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Re: There is a sequence An, such that A1=1，A2=2, and An+2=An+1+An+An1+….+ [#permalink]
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28 Jul 2017, 00:26
==> If A 11=A 10+A 9+A 8+….+A 2+A 1=p, you get A 12 =A 11+A 10+A 11+….+A 2+A 1=2p, and from A 13=4p, A 14=8p, you get A 14:A 11=8p:p=8:1=8. The answer is C. Answer: C
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Re: There is a sequence An, such that A1=1，A2=2, and An+2=An+1+An+An1+….+ [#permalink]
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08 Sep 2017, 10:17
A(1)=1, A(2)=2, A(3)= 3, A(4)=6, A(5)=12 Seq after n>3 is [2^(n3)] *3 Let us say x=3 so A(14)= [(2^13)*x] and A(11)= [(2^8)*x] ratio would be [(2^13)*x] / [(2^8)*x] then it would be just [(2^11)]/[(2^8)]= 2^3
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Re: There is a sequence An, such that A1=1，A2=2, and An+2=An+1+An+An1+….+ [#permalink]
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12 Sep 2017, 18:23
Can you please tell me how derived information for A3



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Re: There is a sequence An, such that A1=1，A2=2, and An+2=An+1+An+An1+….+ [#permalink]
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12 Sep 2017, 21:52
rghvaggarwal wrote: Can you please tell me how derived information for A3 We are given that each next term of the seq if formed by adding all the previous terms. A3= A1+A2
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Re: There is a sequence An, such that A1=1，A2=2, and An+2=An+1+An+An1+….+
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12 Sep 2017, 21:52






