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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, 04:18
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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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Current Student
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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
Answer is A.
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SVP
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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?!!! 
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Senior Manager
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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
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Director
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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
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Director
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Thanks guys! OA is A.
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Cheers, Rahul.
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