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# The sequence a1, a2, a3,…, an is defined by an = an – 2 + an – 1 for a

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Math Expert
Joined: 02 Sep 2009
Posts: 46307
The sequence a1, a2, a3,…, an is defined by an = an – 2 + an – 1 for a [#permalink]

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25 Apr 2017, 03:23
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5% (low)

Question Stats:

95% (01:06) correct 5% (01:47) wrong based on 60 sessions

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The sequence $$a_1$$, $$a_2$$, $$a_3$$, …, $$a_n$$ is defined by $$an = a_{n – 2} + a_{n – 1}$$ for all n > 2 . If $$a_3 = 2$$ and $$a_5 = 5$$, what is the value of $$a_6$$?

(A) 7
(B) 8
(C) 10
(D) 12
(E) 13

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Intern
Joined: 18 Jul 2016
Posts: 16
Re: The sequence a1, a2, a3,…, an is defined by an = an – 2 + an – 1 for a [#permalink]

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25 Apr 2017, 03:31
1
a3=2, a5=5

a5 = a3+a4 = 2+a4 = 5
a4=3

a6=a5+a4 = 5+3 = 8

Correct me if I'm wrong
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Engineer, Quant score 53 First attempt.

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Joined: 12 Dec 2010
Posts: 40
Re: The sequence a1, a2, a3,…, an is defined by an = an – 2 + an – 1 for a [#permalink]

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25 Apr 2017, 03:35
1
a_5 =a_4+a_3
5=a_4 + 2
a_4=3
a_6 = a_5+a_4
a_6=5+3
a_6=8
Ans is B

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Joined: 04 Mar 2011
Posts: 2570
Re: The sequence a1, a2, a3,…, an is defined by an = an – 2 + an – 1 for a [#permalink]

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28 Apr 2017, 15:17
1
Bunuel wrote:
The sequence $$a_1$$, $$a_2$$, $$a_3$$, …, $$a_n$$ is defined by $$an = a_{n – 2} + a_{n – 1}$$ for all n > 2 . If $$a_3 = 2$$ and $$a_5 = 5$$, what is the value of $$a_6$$?

(A) 7
(B) 8
(C) 10
(D) 12
(E) 13

We are given that the nth term of a sequence is defined as: a(n) = a(n-2) + a(n-1).

We know that a(5) = 5 and that a(3) = 2; thus:

a(5) = a(3) + a(4)

5 = 2 + a(4)

3 = a(4)

We need to determine the value of a(6).

a(6) = a(4) + a(5)

a(6) = 3 + 5 = 8

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Re: The sequence a1, a2, a3,…, an is defined by an = an – 2 + an – 1 for a   [#permalink] 28 Apr 2017, 15:17
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