Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

A sequence of numbers a1, a2, a3,…. is defined as follows: a1 = 3, a2 [#permalink]

Show Tags

15 Jun 2016, 01:46

10

45

00:00

A

B

C

D

E

Difficulty:

75% (hard)

Question Stats:

60% (01:37) correct 40% (01:48) wrong based on 1289 sessions

HideShow timer Statistics

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]

Show Tags

15 Jun 2016, 03:27

7

9

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]

Show Tags

15 Jun 2016, 03:49

2

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]

Show Tags

16 Jul 2017, 08:24

3

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 [#permalink]

Show Tags

29 Aug 2017, 22:32

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 [#permalink]

Show Tags

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
_________________

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]

Show Tags

13 Oct 2017, 19:28

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 [#permalink]

Show Tags

15 Nov 2017, 13:49

3

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 [#permalink]

Show Tags

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]

Show Tags

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]

Show Tags

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]

Show Tags

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 [#permalink]

Show Tags

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 ?

many thanks for taking time to explain

enjoy the weekend

gmatclubot

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