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

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Director
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If the sequence X(1), X(2), X(3),...,X(n),..is such that [#permalink]  08 Oct 2005, 03:18
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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

Pls explain your solution. Thanks!
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Cheers, Rahul.

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[#permalink]  08 Oct 2005, 04:25
X(1)=3, X(2)=5, X(3)=9.... difference is squared each time, so:
X(2)-X(1)=2^2+1, X(3)-X(2)=2^3+1....

X(20)=2^20+1
X(19)=2^19+1

2^20 can be rewritten as 2^19*2
2*2^19-2^19=2^19

SVP
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Re: PS - Sequence [#permalink]  08 Oct 2005, 04:26
rahulraao wrote:
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) =

Sorry, but I guess X(n+1)=2X(n)-1 for n >= 1 ,rite?!!!
Senior Manager
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[#permalink]  08 Oct 2005, 08:25
I got A

X(20)-X(19) = 2*(X(19)-X(18)) = 2*2*(X(18)-X(17))
= ... = (2^18) * (X(2)-X(1)) = 2^19
Director
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[#permalink]  08 Oct 2005, 09:43
Ans is A
x(1) = 3
x(2) = 5
x(3) = 9
x(4) = 17

If you see the difference b/w 2 successive numbers, it is 2^(lower n)
i.e, b/w x(3) and (4) = 16 = 2^3

So, x(20)-x(19) = 2^19
Director
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[#permalink]  08 Oct 2005, 19:21
Thanks guys! OA is A.
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Cheers, Rahul.

[#permalink] 08 Oct 2005, 19:21
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# If the sequence X(1), X(2), X(3),...,X(n),..is such that

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