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A sequence of numbers a1, a2, a3,…. is defined as follows: a1 = 3, a2
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15 Jun 2016, 01:46

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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
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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
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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
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16 Jul 2017, 08:24

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3

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
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29 Aug 2017, 22:32

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1

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
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05 Sep 2017, 18:06

1

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

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
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A sequence of numbers a1, a2, a3,…. is defined as follows: a1 = 3, a2
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13 Oct 2017, 19:28

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1

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
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15 Nov 2017, 13:49

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Top Contributor

1

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
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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
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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
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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
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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 sequence of numbers a1, a2, a3,…. is defined as follows: a1 = 3, a2
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05 May 2018, 03:14

Sash143 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) 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

Hello pushpitkc, hope you are having an awesome gmat weekend

i have a few questons regarding the above solution, so let me break it down in into following clauses

1.) it says "Say n = 3 [given n>2]. Hence we must find value of a5" my question what does \(n\) mean is it the last term ? based on which rule do we concude " If n = 3 [given n>2]. Hence we must find value of \(a_5\) i mean why if n = 3 then we need to find \(a_5\) and not for example \(a_6\) ?

2.) if \(a_3 = a_1*a_2 = 3*5 = 15\), then to find \(a_4\) we need to perform following \(a_1*a_2*a_3 = 3*5*15 = 225\)

and following this logic in order to find \(a_5\)we need to do this \(a_1*a_2*a_3*a_4 = 3*5*15*225 = 3375\)

i cant understand why in the solution above to find \(a_5\) we multiply by the same numbers \(a_5= 15*15*15*15 = t^4\), to find the next term shoudlnt we mupltiply by all previous terms

3.) Also based on this solution \(a_5= 15*15*15*15 = t^4\) why the correct answer is \(t^4\) because there are FOUR numbers 15 ? but there could be infinite NUMBERS of 15

And the last question is it geometric sequence question ?