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

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Joined: 02 Sep 2009
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The sequence of numbers S = {s1, s2, s3 …} is defined by s1 = 2, s2 =  [#permalink]

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03 Jul 2018, 09:04
1
1
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Difficulty:

85% (hard)

Question Stats:

45% (01:58) correct 55% (02:22) wrong based on 64 sessions

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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, $$s_3 = 10^2$$. What is the greatest value of n for which $$s_n$$ has 2,000 or fewer digits?

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

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

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03 Jul 2018, 09:17
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S4 = 100^10 = 10^20
S5 = (10^20)^100 = 10^2000

S5 will have 2000 zeros and a 1, hence 2001 digits.

Hence n = 4, Option D.
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Re: The sequence of numbers S = {s1, s2, s3 …} is defined by s1 = 2, s2 =  [#permalink]

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20 Jul 2018, 00:26
Can any expert explain.
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Re: The sequence of numbers S = {s1, s2, s3 …} is defined by s1 = 2, s2 = &nbs [#permalink] 20 Jul 2018, 00:26
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