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# If the sequence x(1), x(2), x(3), , x(n), is such that x(1)

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Director
Joined: 29 Aug 2005
Posts: 808
If the sequence x(1), x(2), x(3), , x(n), is such that x(1)  [#permalink]

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23 Nov 2008, 07:41
If the sequence x(1), x(2), x(3), …, x(n), … is such that x(1) = 3 and x(n+1) = 2x(n) – 1 for n ≥ 1, then x(20) – x(19) =
A. 2^19
B. 2^20
C. 2^21
D. 2^20 - 1
E. 2^21 - 1

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Intern
Joined: 21 Nov 2008
Posts: 4
Re: GMAT Set 27 - 29  [#permalink]

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23 Nov 2008, 07:57
1
A

x(1)=3 = 2^1 + 1
x(2)=5 = 2^2 + 1
x(3)=9 = 2^3 + 1
and so on...
x(19)= 2^19 + 1
x(20)= 2^20 +1
x(20) - x(19) =>2^20 - 2 ^19 = 2^19
Director
Joined: 29 Aug 2005
Posts: 808
Re: GMAT Set 27 - 29  [#permalink]

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23 Nov 2008, 08:28
thanks sapnaprakash for an input!
Although, I can see the trend, is there a more constructive way to deduce that it is x(n)= 2^n+1?

I can see you just joined the club - welcome!

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
Re: GMAT Set 27 - 29 &nbs [#permalink] 23 Nov 2008, 08:28
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# If the sequence x(1), x(2), x(3), , x(n), is such that x(1)

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