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If a sequence is defined by a_n = (a_(n-1))*(a_(n-2)) for all n >=3

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Magoosh GMAT Instructor
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If a sequence is defined by a_n = (a_(n-1))*(a_(n-2)) for all n >=3  [#permalink]

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New post Updated on: 23 Sep 2014, 15:05
1
2
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

81% (01:33) correct 19% (01:22) wrong based on 95 sessions

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If a sequence is defined by \(a_n = (a_{n-1})*(a_{n-2})+1\) for all \(n\geq3\), and if \(a_1 = 1\) and \(a_2 = 1\), what is the 6th term?
(A) 1
(B) 7
(C) 22
(D) 155
(E) 721


For a discussion of questions involving sequences, especially recursive sequences such as this one, as well as the OE for this question, please see:
http://magoosh.com/gmat/2012/sequences-on-the-gmat/

Mike :-)

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Originally posted by mikemcgarry on 23 Sep 2014, 10:26.
Last edited by mikemcgarry on 23 Sep 2014, 15:05, edited 1 time in total.
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Re: If a sequence is defined by a_n = (a_(n-1))*(a_(n-2)) for all n >=3  [#permalink]

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New post 23 Sep 2014, 13:22
1
mikemcgarry wrote:
[color=#0000ff]If a sequence is defined by \(a_n = (a_{n-1})*(a_{n-2})\) for all \(n\geq3\), and if \(a_1 = 1\) and \(a_2 = 1\), what is the 6th term?


As the question is written, the answer would be 1 (every term would be 1). If the correct answer is to be C here, I think you want the definition of the later terms to include a '+1' at the end:

\(a_n = (a_{n-1})*(a_{n-2})\) \(+ 1\) for all \(n\geq3\)
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Re: If a sequence is defined by a_n = (a_(n-1))*(a_(n-2)) for all n >=3  [#permalink]

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New post 23 Sep 2014, 15:06
IanStewart wrote:
mikemcgarry wrote:
[color=#0000ff]If a sequence is defined by \(a_n = (a_{n-1})*(a_{n-2})\) for all \(n\geq3\), and if \(a_1 = 1\) and \(a_2 = 1\), what is the 6th term?


As the question is written, the answer would be 1 (every term would be 1). If the correct answer is to be C here, I think you want the definition of the later terms to include a '+1' at the end:

\(a_n = (a_{n-1})*(a_{n-2})\) \(+ 1\) for all \(n\geq3\)

Ian,
Many thanks, my friend, for catching that typo. Yes, you are 100% correct: with the "+ 1," the sequence would be utterly trivial. I corrected it the original question.
Thanks again!
Mike :-)
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Re: If a sequence is defined by a_n = (a_(n-1))*(a_(n-2)) for all n >=3  [#permalink]

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New post 01 Oct 2014, 01:34
1
\(a_1 = 1\)

\(a_2 = 1\)

\(a_3 = 1 * 1 + 1 = 2\)

\(a_4 = 2*1+1 = 3\)

\(a_5 = 3*2 + 1 = 7\)

\(a_6 = 7*3 + 1 = 22\)

Answer = C
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Re: If a sequence is defined by a_n = (a_(n-1))*(a_(n-2)) for all n >=3  [#permalink]

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New post 08 Dec 2019, 15:43
Hi All,

While this question might appear a bit 'scary', it's just a Sequence question and we're told exactly how the sequence 'works.' We're given the first two terms of the sequence and then told that each term that follows the first two is the (PRODUCT of the prior two terms that come before it in the sequence) plus 1. We're asked for the value of the 6th term. In these types of questions, it's usually fairly easy (and necessary) to calculate all of the terms in the sequence.

1st = 1
2nd = 1
3rd = (2nd term)(1st term) + 1 = (1)(1) + 1 = 2
4th = (3rd term)(2nd term) + 1 = (2)(1) + 1 = 3
5th = (4th term)(3rd term) + 1 = (3)(2) + 1 = 7
6th = (5th term)(4th term) + 1 = (7)(3) + 1 = 22

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Re: If a sequence is defined by a_n = (a_(n-1))*(a_(n-2)) for all n >=3   [#permalink] 08 Dec 2019, 15:43
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