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# There is a sequence An, such that A1=1，A2=2, and An+2=An+1+An+An-1+….+

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There is a sequence An, such that A1=1，A2=2, and An+2=An+1+An+An-1+….+  [#permalink]

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26 Jul 2017, 01:14
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There is a sequence An, such that A1=1，A2=2, and An+2=An+1+An+An-1+….+A2+A1. What is the ratio of A14 to A11?

A. 32
B. 16
C. 8
D. 4
E. 2

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"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" BSchool Forum Moderator Joined: 26 Feb 2016 Posts: 2948 Location: India GPA: 3.12 There is a sequence An, such that A1=1，A2=2, and An+2=An+1+An+An-1+….+ [#permalink] ### Show Tags 26 Jul 2017, 01:26 2 We know that An+2=An+1+An+An-1+….+A2+A1 Given data: A1=1 and A2=2 From the above information, A3 = A1 + A2 = 1 + 2 = 3 Similarly, A4 = 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 A14 to A11 is $$\frac{384*16}{384*2}$$ = 8(Option C) _________________ You've got what it takes, but it will take everything you've got Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 5866 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: There is a sequence An, such that A1=1，A2=2, and An+2=An+1+An+An-1+….+ [#permalink] ### Show Tags 28 Jul 2017, 01:26 ==> If A11=A10+A9+A8+….+A2+A1=p, you get A12 =A11+A10+A11+….+A2+A1=2p, and from A13=4p, A14=8p, you get A14:A11=8p:p=8:1=8. The answer is C. Answer: C _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
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Re: There is a sequence An, such that A1=1，A2=2, and An+2=An+1+An+An-1+….+  [#permalink]

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08 Sep 2017, 11:17
A(1)=1, A(2)=2, A(3)= 3, A(4)=6, A(5)=12
Seq after n>3 is [2^(n-3)] *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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Abhimanyu

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Re: There is a sequence An, such that A1=1，A2=2, and An+2=An+1+An+An-1+….+  [#permalink]

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12 Sep 2017, 19:23
Can you please tell me how derived information for A3
Intern
Joined: 14 Oct 2016
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Re: There is a sequence An, such that A1=1，A2=2, and An+2=An+1+An+An-1+….+  [#permalink]

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12 Sep 2017, 22:52
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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Abhimanyu

Re: There is a sequence An, such that A1=1，A2=2, and An+2=An+1+An+An-1+….+ &nbs [#permalink] 12 Sep 2017, 22:52
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