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Let a be a sequence such that the term an=a(n−1)+a(n−3) for all intege

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Bunuel
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Let a be a sequence such that the term an=a(n−1)+a(n−3) for all intege [#permalink] New post   30 Nov 2016, 02:54
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Let a be a sequence such that the term \(a_n=a_{(n−1)}+a_{(n−3)}\) for all integers n>3. If \(a_1=1\), \(a_2=5\), and \(a_4=9\), what is the value of \(a_6\)?

A. 4
B. 6
C. 14
D. 22
E. 23
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Re: Let a be a sequence such that the term an=a(n−1)+a(n−3) for all intege [#permalink] New post   30 Nov 2016, 23:07
a6 = a5 + a3

a4 = a3 + a1 --> a3 = 8

a5 = a4 + a2 = 9 + 5 = 14

a6 = 14 + 8 = 22

Answer: D
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Re: Let a be a sequence such that the term an=a(n−1)+a(n−3) for all intege [#permalink] New post   21 Jan 2017, 02:06
Bunuel wrote:
Let a be a sequence such that the term \(a_n=a_{(n−1)}+a_{(n−3)}\) for all integers n>3. If \(a_1=1\), \(a_2=5\), and \(a_4=9\), what is the value of \(a_6\)?

A. 4
B. 6
C. 14
D. 22
E. 23



\(a_6=a_3+a_5\)
\(a_5=a_4+a_2\)=9+5=14
\(a_4=a_3+a_1\) => 9=\(a_3\)+1 = >\(a_3\) =8;
\(a_6=8+14=22\)

Hence option D is correct.
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Re: Let a be a sequence such that the term an=a(n−1)+a(n−3) for all intege [#permalink] New post   16 Mar 2017, 15:35
Bunuel wrote:
Let a be a sequence such that the term \(a_n=a_{(n−1)}+a_{(n−3)}\) for all integers n>3. If \(a_1=1\), \(a_2=5\), and \(a_4=9\), what is the value of \(a_6\)?

A. 4
B. 6
C. 14
D. 22
E. 23


In order to solve this question we must know what the value of a3 is and a4; we can reverse engineer this problem

a4=a3 + a1
a5 = a4 + a2 (this is logical because these are our two given values)
a5= 9 + 5
a6= 14 + a3

9=a3 + 1
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Re: Let a be a sequence such that the term an=a(n−1)+a(n−3) for all intege [#permalink] New post   21 Mar 2017, 06:18
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Bunuel wrote:
Let a be a sequence such that the term \(a_n=a_{(n−1)}+a_{(n−3)}\) for all integers n>3. If \(a_1=1\), \(a_2=5\), and \(a_4=9\), what is the value of \(a_6\)?

A. 4
B. 6
C. 14
D. 22
E. 23


We are given the sequence a(n) = a(n-1) + a(n-3) and that a(1) = 1, a(2) = 5, and a(4) = 9.

To get a(6), we need to know the value of a(5) and a(3). Let’s first determine the value of a(3):

a(4) = a(3) + a(1)

9 = a(3) + 1

a(3) = 8

Now we can determine a(5):

a(5) = a(4) + a(2)

a(5) = 9 + 5 = 14

Finally, we can determine a(6):

a(6) = a(5) + a(3)

a(6) = 14 + 8 = 22

Answer: D
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Re: Let a be a sequence such that the term an=a(n−1)+a(n−3) for all intege [#permalink]
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