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A sequence of numbers \(a_1\), \(a_2\), \(a_3\),…. is defined as follows: \(a_1 = 3\), \(a_2 = 5\), and every term in the sequence after \(a_2\) is the product of all terms in the sequence preceding it, e.g, \(a_3 = (a_1)(a_2)\) and \(a4 = (a_1)(a_2)(a_3)\). If \(a_n =t\) and \(n > 2\), what is the value of \(a_{n+2}\) in terms of t?
Re: A sequence of numbers a1, a2, a3,…. is defined as follows: a1 = 3, a2 [#permalink]
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15 Jun 2016, 03:27
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Bunuel wrote:
A sequence of numbers \(a_1\), \(a_2\), \(a_3\),…. is defined as follows: \(a_1 = 3\), a_2 = 5, and every term in the sequence after \(a_2\) is the product of all terms in the sequence preceding it, e.g, \(a_3 = (a_1)(a_2)\) and \(a4 = (a_1)(a_2)(a_3)\). If \(a_n =t\) and \(n > 2\), what is the value of \(a_{n+2}\) in terms of t?
A) 4t B) t^2 C) t^3 D) t^4 E) t^8
Given \(a_n = t\) This means \(a_1 * a_2 * a_3* ..... a_{n-1} = t\)
Re: A sequence of numbers a1, a2, a3,…. is defined as follows: a1 = 3, a2 [#permalink]
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15 Jun 2016, 03:49
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Bunuel wrote:
A sequence of numbers \(a_1\), \(a_2\), \(a_3\),…. is defined as follows: \(a_1 = 3\), a_2 = 5, and every term in the sequence after \(a_2\) is the product of all terms in the sequence preceding it, e.g, \(a_3 = (a_1)(a_2)\) and \(a4 = (a_1)(a_2)(a_3)\). If \(a_n =t\) and \(n > 2\), what is the value of \(a_{n+2}\) in terms of t?
A) 4t B) t^2 C) t^3 D) t^4 E) t^8
\(a_n = (a_1)(a_2)........(a_{n-1})\) = t
\(a_{n+1}\) = \((a_1)(a_2)........(a_n)\) = \((a_1)(a_2)........(a_{n-1})\)*\(a_n\) = t *t = \(t^2\)
Re: A sequence of numbers a1, a2, a3,…. is defined as follows: a1 = 3, a2 [#permalink]
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16 Jul 2017, 08:24
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Bunuel wrote:
A sequence of numbers \(a_1\), \(a_2\), \(a_3\),…. is defined as follows: \(a_1 = 3\), a_2 = 5, and every term in the sequence after \(a_2\) is the product of all terms in the sequence preceding it, e.g, \(a_3 = (a_1)(a_2)\) and \(a4 = (a_1)(a_2)(a_3)\). If \(a_n =t\) and \(n > 2\), what is the value of \(a_{n+2}\) in terms of t?
A) 4t B) t^2 C) t^3 D) t^4 E) t^8
Say n = 3 [given n>2]. Hence we must find value of a5
Re: A sequence of numbers a1, a2, a3,…. is defined as follows: a1 = 3, a2 [#permalink]
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29 Aug 2017, 22:32
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Bunuel wrote:
A sequence of numbers \(a_1\), \(a_2\), \(a_3\),…. is defined as follows: \(a_1 = 3\), \(a_2 = 5\), and every term in the sequence after \(a_2\) is the product of all terms in the sequence preceding it, e.g, \(a_3 = (a_1)(a_2)\) and \(a4 = (a_1)(a_2)(a_3)\). If \(a_n =t\) and \(n > 2\), what is the value of \(a_{n+2}\) in terms of t?
A sequence of numbers \(a_1\), \(a_2\), \(a_3\),…. is defined as follows: \(a_1 = 3\), \(a_2 = 5\), and every term in the sequence after \(a_2\) is the product of all terms in the sequence preceding it, e.g, \(a_3 = (a_1)(a_2)\) and \(a4 = (a_1)(a_2)(a_3)\). If \(a_n =t\) and \(n > 2\), what is the value of \(a_{n+2}\) in terms of t?
(A) 4t (B) t^2 (C) t^3 (D) t^4 (E) t^8
We are given a sequence in which every term in the sequence after a(2) is the product of all terms in the sequence preceding it. So:
a(n+1) = a(n) x a(n-1) x ... x a(2) x a(1)
By the same reasoning, we have:
a(n) = a(n-1) x a(n-2) x ... x a(2) x a(1)
We can substitute a(n-1) x... x a(2) x a(1) in the a(n+1) equation for a(n), so we have a(n+1) = a(n) x a(n).
However, recall that a(n) = t, so a(n+1) = t x t = t^2. By the same reasoning, we have:
a(n+2) = a(n+1) x a(n) x a(n-1) x ... x a(2) x a(1)
However, a(n) x a(n-1) x .... x a(2) x a(1) = a(n+1) and a(n+1) = t^2, so:
a(n+2) = a(n+1) x a(n+1) = t^2 x t^2 = t^4
Answer: D
_________________
Jeffery Miller Head of GMAT Instruction
GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions
A sequence of numbers a1, a2, a3,…. is defined as follows: a1 = 3, a2 [#permalink]
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13 Oct 2017, 19:28
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Bunuel wrote:
A sequence of numbers \(a_1\), \(a_2\), \(a_3\),…. is defined as follows: \(a_1 = 3\), \(a_2 = 5\), and every term in the sequence after \(a_2\) is the product of all terms in the sequence preceding it, e.g, \(a_3 = (a_1)(a_2)\) and \(a4 = (a_1)(a_2)(a_3)\). If \(a_n =t\) and \(n > 2\), what is the value of \(a_{n+2}\) in terms of t?
A sequence of numbers \(a_1\), \(a_2\), \(a_3\),…. is defined as follows: \(a_1 = 3\), \(a_2 = 5\), and every term in the sequence after \(a_2\) is the product of all terms in the sequence preceding it, e.g, \(a_3 = (a_1)(a_2)\) and \(a4 = (a_1)(a_2)(a_3)\). If \(a_n =t\) and \(n > 2\), what is the value of \(a_{n+2}\) in terms of t?
Re: A sequence of numbers a1, a2, a3,…. is defined as follows: a1 = 3, a2 [#permalink]
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02 Jan 2018, 05:58
Bunuel wrote:
A sequence of numbers \(a_1\), \(a_2\), \(a_3\),…. is defined as follows: \(a_1 = 3\), \(a_2 = 5\), and every term in the sequence after \(a_2\) is the product of all terms in the sequence preceding it, e.g, \(a_3 = (a_1)(a_2)\) and \(a4 = (a_1)(a_2)(a_3)\). If \(a_n =t\) and \(n > 2\), what is the value of \(a_{n+2}\) in terms of t?
(A) 4t (B) t^2 (C) t^3 (D) t^4 (E) t^8
Bunuel - can I call the above mentioned problem as a recursive sequence ? I know this formula An= n1+(n-1)*d but could not apply it here.
Re: A sequence of numbers a1, a2, a3,…. is defined as follows: a1 = 3, a2 [#permalink]
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02 Jan 2018, 06:00
hazelnut wrote:
Bunuel wrote:
A sequence of numbers \(a_1\), \(a_2\), \(a_3\),…. is defined as follows: \(a_1 = 3\), \(a_2 = 5\), and every term in the sequence after \(a_2\) is the product of all terms in the sequence preceding it, e.g, \(a_3 = (a_1)(a_2)\) and \(a4 = (a_1)(a_2)(a_3)\). If \(a_n =t\) and \(n > 2\), what is the value of \(a_{n+2}\) in terms of t?
A sequence of numbers a1, a2, a3,…. is defined as follows: a1 = 3, a2 [#permalink]
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02 Jan 2018, 06:39
dave13 wrote:
hazelnut wrote:
Bunuel wrote:
A sequence of numbers \(a_1\), \(a_2\), \(a_3\),…. is defined as follows: \(a_1 = 3\), \(a_2 = 5\), and every term in the sequence after \(a_2\) is the product of all terms in the sequence preceding it, e.g, \(a_3 = (a_1)(a_2)\) and \(a4 = (a_1)(a_2)(a_3)\). If \(a_n =t\) and \(n > 2\), what is the value of \(a_{n+2}\) in terms of t?
Re: A sequence of numbers a1, a2, a3,…. is defined as follows: a1 = 3, a2 [#permalink]
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20 Mar 2018, 22:33
Bunuel wrote:
A sequence of numbers \(a_1\), \(a_2\), \(a_3\),…. is defined as follows: \(a_1 = 3\), \(a_2 = 5\), and every term in the sequence after \(a_2\) is the product of all terms in the sequence preceding it, e.g, \(a_3 = (a_1)(a_2)\) and \(a4 = (a_1)(a_2)(a_3)\). If \(a_n =t\) and \(n > 2\), what is the value of \(a_{n+2}\) in terms of t?
(A) 4t (B) t^2 (C) t^3 (D) t^4 (E) t^8
an = t = .......(an - 1)
(an + 1) = .......(an - 1) * an = t^2
(an + 2) = .....(an - 1) * an * (an + 1)
=) t^2 * t ^2 = t^4 = D the answer
thanks
gmatclubot
Re: A sequence of numbers a1, a2, a3,…. is defined as follows: a1 = 3, a2
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20 Mar 2018, 22:33
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60% (01:38) correct 
I know this formula An= n1+(n-1)*d but could not apply it here.
