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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. # In a certain sequence , term[color=red]1[/color] = 64  Question banks Downloads My Bookmarks Reviews Important topics
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TAGS: GRE Instructor Joined: 10 Apr 2015
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In a certain sequence , term[color=red]1[/color] = 64 [#permalink]
1
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Expert's post 00:00

Question Stats: 68% (02:08) correct 31% (01:36) wrong based on 35 sessions
In a certain sequence, term1 = 64, and for all n > 1, termn = (2^n)(termn-1)
What is the value of term11/term8 ?

A) 2^3
B) 2^6
C) 2^9
D) 2^27
E) 2^30
[Reveal] Spoiler: OA

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Brent Hanneson – Creator of greenlighttestprep.com
If you enjoy my solutions, you'll like my GRE prep course. Intern Joined: 06 Feb 2018
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Re: In a certain sequence , term[color=red]1[/color] = 64 [#permalink] GRE Instructor Joined: 10 Apr 2015
Posts: 3826
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Kudos [?]: 4470  , given: 69

Re: In a certain sequence , term[color=red]1[/color] = 64 [#permalink]
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Expert's post
sam_ridhi wrote:

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com
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Re: In a certain sequence , term[color=red]1[/color] = 64 [#permalink]
how's it E?
GRE Instructor Joined: 10 Apr 2015
Posts: 3826
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Kudos [?]: 4470 , given: 69

Re: In a certain sequence , term[color=red]1[/color] = 64 [#permalink]
Expert's post
Sona4292 wrote:
how's it E?

I'll post a solution in 2 days.
In the meantime, see you do with the question.

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com
If you enjoy my solutions, you'll like my GRE prep course.  Active Member  Joined: 07 Jan 2018
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Kudos [?]: 769  , given: 88

Re: In a certain sequence , term[color=red]1[/color] = 64 [#permalink]
1
KUDOS
The first term of the sequence is given as 64 = 2^6
From the formula,
2nd term = $$2^2 * 2^6$$
3rd term = $$2^3 * 2^2 * 2^6$$
4th term = $$2^4 * 2^3 * 2^2 * 2^6$$

There is a pattern with 2^6 constant for every term and the power of 2 is raised consecutively from $$2^2 to 2^n$$

Hence, $$2^1^1 = 2^6 * 2^2 * 2^3 ...........*2^1^1$$
similarly $$2^8 = 2^6 * 2^2 * 2^3.........*2^8$$

when finding the ratio everything cancels leaving only $$2^9 * 2^10 * 2^1^1 = 2^3^0$$
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This is my response to the question and may be incorrect. Feel free to rectify any mistakes
Need Practice? 20 Free GRE Quant Tests available for free with 20 Kudos GRE Instructor Joined: 10 Apr 2015
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Kudos [?]: 4470  , given: 69

Re: In a certain sequence , term[color=red]1[/color] = 64 [#permalink]
1
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Expert's post
GreenlightTestPrep wrote:
In a certain sequence, term1 = 64, and for all n > 1, termn = (2^n)(termn-1)
What is the value of term11/term8 ?

A) 2^3
B) 2^6
C) 2^9
D) 2^27
E) 2^30

*kudos for all correct solutions[/quote]

Let's list a few terms and look for a pattern

term1 = 64 = 2^6
term2 = (2^6)(2^2)
term3 = (2^6)(2^2)(2^3)
term4 = (2^6)(2^2)(2^3)(2^4)
.
.
.
term8 = (2^6)(2^2)(2^3)(2^4)(2^5)(2^6)(2^7)(2^8)
.
.
.
term11 = (2^6)(2^2)(2^3)(2^4)(2^5)(2^6)(2^7)(2^8)(2^9)(2^10)(2^11)

So, term11/term8 = (2^6)(2^2)(2^3)(2^4)(2^5)(2^6)(2^7)(2^8)(2^9)(2^10)(2^11)/(2^6)(2^2)(2^3)(2^4)(2^5)(2^6)(2^7)(2^8)
= (2^9)(2^10)(2^11)
= 2^30

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com
If you enjoy my solutions, you'll like my GRE prep course. Director Joined: 09 Nov 2018
Posts: 505
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Kudos [?]: 55 , given: 1

Re: In a certain sequence , term[color=red]1[/color] = 64 [#permalink]
GreenlightTestPrep wrote:
GreenlightTestPrep wrote:
In a certain sequence, term1 = 64, and for all n > 1, termn = (2^n)(termn-1)
What is the value of term11/term8 ?

A) 2^3
B) 2^6
C) 2^9
D) 2^27
E) 2^30

*kudos for all correct solutions

Let's list a few terms and look for a pattern

term1 = 64 = 2^8
term2 = (2^8)(2^2)
term3 = (2^8)(2^2)(2^3)
term4 = (2^8)(2^2)(2^3)(2^4)
.
.
.
term8 = (2^8)(2^2)(2^3)(2^4)(2^5)(2^6)(2^7)(2^8)
.
.
.
term11 = (2^8)(2^2)(2^3)(2^4)(2^5)(2^6)(2^7)(2^8)(2^9)(2^10)(2^11)

So, term11/term8 = (2^8)(2^2)(2^3)(2^4)(2^5)(2^6)(2^7)(2^8)(2^9)(2^10)(2^11)/(2^8)(2^2)(2^3)(2^4)(2^5)(2^6)(2^7)(2^8)
= (2^9)(2^10)(2^11)
= 2^30

Cheers,
Brent[/quote]

64=2^8 or 2^6
GRE Instructor Joined: 10 Apr 2015
Posts: 3826
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Kudos [?]: 4470 , given: 69

Re: In a certain sequence , term[color=red]1[/color] = 64 [#permalink]
Expert's post
Good catch!
Rookie mistake on my part.
64 = 2^6 (not 2^8)

That said, the two expressions with 2^8 (or 2^6) cancel each other out. So, fortunately, the solution still worked out Cheers and thanks for the heads up!
I have edited my answer accordingly.

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com
If you enjoy my solutions, you'll like my GRE prep course.  Re: In a certain sequence , term[color=red]1[/color] = 64   [#permalink] 20 Nov 2018, 16:21
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