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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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Kudos [?]: 2190  , given: 26

In a certain sequence , term[color=red]1[/color] = 64 [#permalink]
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Expert's post 00:00

Question Stats: 63% (01:24) correct 36% (01:04) wrong based on 19 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 Sign up for my free GRE Question of the Day emails

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Re: In a certain sequence , term[color=red]1[/color] = 64 [#permalink]
The answer is E? GRE Instructor Joined: 10 Apr 2015
Posts: 2303
Followers: 72

Kudos [?]: 2190  , given: 26

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

Sorry, I didn't add the correct answer.
Yes, the answer is E.

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com Sign up for my free GRE Question of the Day emails

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Re: In a certain sequence , term[color=red]1[/color] = 64 [#permalink]
how's it E?
please explain.
GRE Instructor Joined: 10 Apr 2015
Posts: 2303
Followers: 72

Kudos [?]: 2190 , given: 26

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

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 Sign up for my free GRE Question of the Day emails Director  Joined: 07 Jan 2018
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Re: In a certain sequence , term[color=red]1[/color] = 64 [#permalink]
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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 GRE Instructor Joined: 10 Apr 2015
Posts: 2303
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Kudos [?]: 2190  , given: 26

Re: In a certain sequence , term[color=red]1[/color] = 64 [#permalink]
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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

Answer: E

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com Sign up for my free GRE Question of the Day emails

Director Joined: 09 Nov 2018
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Kudos [?]: 39 , 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

Answer: E

Cheers,
Brent[/quote]

64=2^8 or 2^6
GRE Instructor Joined: 10 Apr 2015
Posts: 2303
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Kudos [?]: 2190 , given: 26

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
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Brent Hanneson – Creator of greenlighttestprep.com Sign up for my free GRE Question of the Day emails Re: In a certain sequence , term[color=red]1[/color] = 64   [#permalink] 20 Nov 2018, 16:21
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