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# The sequence of numbers S={s1,s2,s3…} is defined by s1 = 2,

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Joined: 07 Jun 2014
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The sequence of numbers S={s1,s2,s3…} is defined by s1 = 2, [#permalink]  27 Mar 2018, 16:17
Expert's post
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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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Manager
Joined: 27 Sep 2017
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Kudos [?]: 29 [1] , given: 4

Re: The sequence of numbers S={s1,s2,s3…} is defined by s1 = 2, [#permalink]  27 Mar 2018, 21:34
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~
GMAT Club Legend
Joined: 07 Jun 2014
Posts: 4749
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 93

Kudos [?]: 1659 [0], given: 396

Re: The sequence of numbers S={s1,s2,s3…} is defined by s1 = 2, [#permalink]  04 Apr 2018, 15:42
Expert's post
Fixed..
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Sandy
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GMAT Club Legend
Joined: 07 Jun 2014
Posts: 4749
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 93

Kudos [?]: 1659 [0], given: 396

Re: The sequence of numbers S={s1,s2,s3…} is defined by s1 = 2, [#permalink]  04 Apr 2018, 15:46
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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Re: The sequence of numbers S={s1,s2,s3…} is defined by s1 = 2,   [#permalink] 04 Apr 2018, 15:46
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