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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. # The sequence of numbers S={s1,s2,s3…} is defined by s1 = 2,  Question banks Downloads My Bookmarks Reviews Important topics
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GRE Prep Club Legend  Joined: 07 Jun 2014
Posts: 4857
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
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The sequence of numbers S={s1,s2,s3…} is defined by s1 = 2, [#permalink]
Expert's post 00:00

Question Stats: 75% (00:23) correct 25% (00:00) wrong based on 4 sessions
The sequence of numbers S={s1,s2,s3…} is defined by $$s_{1} = 2$$, $$s_{2} = 10$$, and $$S_{n}=S_{n-1}^{S_{n-2}}$$for each positive integer n greater than or equal to 3. For example, s3 = 102. What is the greatest value of n for which sn has 2,000 or fewer digits?

A. 100
B. 20
C. 5
D. 4
E. 3

Drill 1
Question: 10
Page: 548
[Reveal] Spoiler: OA

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Sandy
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Try our free Online GRE Test Manager Joined: 27 Sep 2017
Posts: 112
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Re: The sequence of numbers S={s1,s2,s3…} is defined by s1 = 2, [#permalink]
1
KUDOS
sandy wrote:
The sequence of numbers S={s1,s2,s3…} is defined by s1 = 2, s2 = 10, and for each positive integer n greater than or equal to 3. For example, s3 = 102. What is the greatest value
of n for which sn has 2,000 or fewer digits?

A. 100
B. 20
C. 5
D. 4
E. 3

Drill 1
Question: 10
Page: 548

I think something is missing especially the defintion of the the sequence, check it out please~
GRE Prep Club Legend  Joined: 07 Jun 2014
Posts: 4857
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 105

Kudos [?]: 1782 , given: 397

Re: The sequence of numbers S={s1,s2,s3…} is defined by s1 = 2, [#permalink]
Expert's post
Fixed..
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Sandy
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Try our free Online GRE Test

GRE Prep Club Legend  Joined: 07 Jun 2014
Posts: 4857
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 105

Kudos [?]: 1782 , given: 397

Re: The sequence of numbers S={s1,s2,s3…} is defined by s1 = 2, [#permalink]
Expert's post
Explanation

Decoding the definition of the sequence tells you that, to find the value of each term, you take the previous term, and raise it to the power of the term before it. You know

$$S_{3}=10^2=100$$ and $$S_{4}=100^{10}=10^{20}$$ and $$S_{5}=(10^{20})^{100}=10^{2000}$$.

So $$S_{4}$$ is the digit 1 followed by twenty zeroes, which is a total of 21 digits, and $$S_{5}$$ is the digit 1 followed by 2,000 zeroes, for a total of 2,001 digits. So the fourth term is the one that meets the condition set forth in the question, and the answer is choice (D).
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Sandy
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Try our free Online GRE Test Re: The sequence of numbers S={s1,s2,s3…} is defined by s1 = 2,   [#permalink] 04 Apr 2018, 15:46
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