Number sequence : PS Archive
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# Number sequence

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Senior Manager
Joined: 21 Jul 2009
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Location: New York, NY
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24 Aug 2009, 17:22
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[Reveal] Spoiler:
A

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Manager
Joined: 10 Aug 2009
Posts: 130
Followers: 3

Kudos [?]: 67 [0], given: 10

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24 Aug 2009, 18:48
$$x_1=3$$

$$x_2=2\times3-1$$

$$x_3=2\times(2\times3-1)-1=2^2\times3-3$$

$$x_4=2\times(2^2\times3-3)-1=2^3\times3-7$$

testing the difference between:

$$x_3-x_2=2^2$$

$$x_4-x_3=2^3$$

there is a pattern : $$x_n-x_{n-1}=2^{n-1}$$

therefore, $$x_{20}-x_{19}=2^{19}$$
Manager
Joined: 28 Jul 2009
Posts: 124
Location: India
Schools: NUS, NTU, SMU, AGSM, Melbourne School of Business
Followers: 6

Kudos [?]: 75 [0], given: 12

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24 Aug 2009, 21:37
LenaA wrote:
$$x_1=3$$

$$x_2=2\times3-1$$

$$x_3=2\times(2\times3-1)-1=2^2\times3-3$$

$$x_4=2\times(2^2\times3-3)-1=2^3\times3-7$$

testing the difference between:

$$x_3-x_2=2^2$$

$$x_4-x_3=2^3$$

there is a pattern : $$x_n-x_{n-1}=2^{n-1}$$

therefore, $$x_{20}-x_{19}=2^{19}$$

Nice explaination.
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Re: Number sequence   [#permalink] 24 Aug 2009, 21:37
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