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The sequence a1, a2, a3, ... ,an, ... is such that an = an-1 [#permalink]
14 Jun 2012, 01:38

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Question Stats:

76% (02:19) correct
24% (01:05) wrong based on 435 sessions

The sequence a_1, a_2, a_3, ... , a_n, ... is such that a_n=\frac{a_{n-1}+a_{n-2}}{2} for all n\geq{3}. If a_3 = 4 and a_5 = 20, what is the value of a_6 ?

(A) 12 (B) 16 (C) 20 (D) 24 (E) 28

Diagnostic Test Question: 3 Page: 20 Difficulty: 600

Re: The sequence a1, a2, a3, ... ,an, ... is such that an = an-1 [#permalink]
14 Jun 2012, 01:39

1

This post received KUDOS

Expert's post

SOLUTION

The sequence a_1, a_2, a_3, ... , a_n, ... is such that a_n=\frac{a_{n-1}+a_{n-2}}{2} for all n\geq{3}. If a_3 = 4 and a_5 = 20, what is the value of a_6 ?

(A) 12 (B) 16 (C) 20 (D) 24 (E) 28

Since given that a_n=\frac{a_{n-1}+a_{n-2}}{2}, then:

Re: The sequence a1, a2, a3, ... ,an, ... is such that an = an-1 [#permalink]
14 Jun 2012, 04:58

1

This post received KUDOS

Hi,

This one has be solved step by step, and there is chance of making mistakes.

Difficulty level: 600

a_n=\frac{a_{n-1}+a_{n-2}}2 or a_n is the average of last two terms, thus, \frac{a_3+a_4}2=a_5 \frac{a_4+a_5}2=a_6 Subtracting these equations; \frac{a_5-a_3}2=a_6-a_5 a_6=\frac{3a_5-a_3}2=\frac{3*20-4}2=28

Re: The sequence a1, a2, a3, ... ,an, ... is such that an = an-1 [#permalink]
22 Jun 2012, 01:38

Expert's post

SOLUTION

The sequence a_1, a_2, a_3, ... , a_n, ... is such that a_n=\frac{a_{n-1}+a_{n-2}}{2} for all n\geq{3}. If a_3 = 4 and a_5 = 20, what is the value of a_6 ?

(A) 12 (B) 16 (C) 20 (D) 24 (E) 28

Since given that a_n=\frac{a_{n-1}+a_{n-2}}{2}, then:

Re: The sequence a1, a2, a3, ... ,an, ... is such that an = an-1 [#permalink]
14 Jul 2014, 19:56

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Re: The sequence a1, a2, a3, ... ,an, ... is such that an = an-1 [#permalink]
27 Aug 2014, 16:26

Bunuel wrote:

The sequence a_1, a_2, a_3, ... , a_n, ... is such that a_n=\frac{a_{n-1}+a_{n-2}}{2} for all n\geq{3}. If a_3 = 4 and a_5 = 20, what is the value of a_6 ?

(A) 12 (B) 16 (C) 20 (D) 24 (E) 28

Diagnostic Test Question: 3 Page: 20 Difficulty: 600

Nice but easy problem. I think the idea is based on Fibonacci sequence.

gmatclubot

Re: The sequence a1, a2, a3, ... ,an, ... is such that an = an-1
[#permalink]
27 Aug 2014, 16:26

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