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# An infinite sequence a1,a2,a3,…an can be defined as an=3n–an−1 , wher

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Math Expert
Joined: 02 Sep 2009
Posts: 52119
An infinite sequence a1,a2,a3,…an can be defined as an=3n–an−1 , wher  [#permalink]

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17 Apr 2018, 04:27
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Difficulty:

15% (low)

Question Stats:

87% (01:27) correct 13% (01:20) wrong based on 66 sessions

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An infinite sequence $$a_1$$, $$a_2$$, $$a_3$$, … $$a_n$$ can be defined as $$a_n=3n–a_{n−1}$$, where n > 1 and $$a_1 = 1$$. Which of the following represents the first 5 terms of the sequence?

A. 1, 5, 4, 8, 16
B. 1, 5, 4, 8, 7
C. 1, 6, 10, 2, 13
D. 1, 2, 3, 5, 10
E. 1, 7, 16, 28, 43

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Joined: 30 May 2017
Posts: 134
Location: United States
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Re: An infinite sequence a1,a2,a3,…an can be defined as an=3n–an−1 , wher  [#permalink]

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17 Apr 2018, 04:40
Bunuel wrote:
An infinite sequence $$a_1$$, $$a_2$$, $$a_3$$, … $$a_n$$ can be defined as $$a_n=3n–a_{n−1}$$, where n > 1 and $$a_1 = 1$$. Which of the following represents the first 5 terms of the sequence?

A. 1, 5, 4, 8, 16
B. 1, 5, 4, 8, 7
C. 1, 6, 10, 2, 13
D. 1, 2, 3, 5, 10
E. 1, 7, 16, 28, 43

$$a_1$$ = 1
$$a_2$$ = 3(2) -1 = 5
$$a_3$$ = 3(3) -5 = 4
$$a_4$$ = 3(4) -4 = 8
$$a_5$$ = 3(5) -8 = 7

Hence option B = 1, 5, 4, 8, 7 is the answer.
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An infinite sequence a1,a2,a3,…an can be defined as an=3n–an−1 , wher  [#permalink]

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17 Apr 2018, 09:30
Looks to me like a straight forward question without much of a twist.
However I could be wrong!
We know a1 = 1, a2= 3*2-a1 = 3*2-1 = 5
a3 = 3*3 - a1 =9-5 = 4
a4 = 3*4-a3 = 12-4 = 8
a5 = 3*5 - a4 = 15-8 = 7
Option B
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Re: An infinite sequence a1,a2,a3,…an can be defined as an=3n–an−1 , wher  [#permalink]

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19 Apr 2018, 15:52
Bunuel wrote:
An infinite sequence $$a_1$$, $$a_2$$, $$a_3$$, … $$a_n$$ can be defined as $$a_n=3n–a_{n−1}$$, where n > 1 and $$a_1 = 1$$. Which of the following represents the first 5 terms of the sequence?

A. 1, 5, 4, 8, 16
B. 1, 5, 4, 8, 7
C. 1, 6, 10, 2, 13
D. 1, 2, 3, 5, 10
E. 1, 7, 16, 28, 43

We are given that a_n = 3n - a_(n-1)

The first term is a_1 = 1

For n = 2, we have a_2 = 3(2) - 1 = 5

For n = 3, we have a_3 = 3(3) - 5 = 4

For n = 4, we have a_4 = 3(4) - 4 = 8

For n = 5, we have a_5 = 3(5) - 8 = 7

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Re: An infinite sequence a1,a2,a3,…an can be defined as an=3n–an−1 , wher &nbs [#permalink] 19 Apr 2018, 15:52
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