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# If the sequence x1, x2,x3,...,xn is such that X1=3 and Xn+1

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If the sequence x1, x2,x3,...,xn is such that X1=3 and Xn+1 [#permalink]  06 May 2008, 11:05
If the sequence x1, x2,x3,...,xn is such that X1=3 and Xn+1 = 2Xn - 1 for n=1, then X20-X19=?

a) 2^19
b) 2^20
c) 2^21
d) 2^20 -1
e) 2^21 -1
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Re: sequence [#permalink]  06 May 2008, 11:27
hmm it took me a long time ... but lets try this ...

start writing out some of the resultants and should start seeing a pattern where each value corresponds to 2^xn + 1 ... therefore :

x20-x19 corresponds to (2^20 + 1) - (2^19 + 1) = 2^20- 2^19 = 2^19 (2-1) = 2^19

OA?

puma wrote:
If the sequence x1, x2,x3,...,xn is such that X1=3 and Xn+1 = 2Xn - 1 for n=1, then X20-X19=?

a) 2^19
b) 2^20
c) 2^21
d) 2^20 -1
e) 2^21 -1

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Re: sequence [#permalink]  06 May 2008, 11:28

Xn+1 = 2Xn -1 ,X1=3

X2 = 3*2 -1 = 5 (X2-X1 = 2) 2^1

X3 =5*2 -1 = 9 (X3-X2 =4 ) 2^2

X4 = 9*2 -1 =17 (X4-X3 = 8 ) 2^3

So we have a pattern where Xn - Xn-1 =2^n-1

Therefore for X20 -X19 = 2^19
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Re: sequence [#permalink]  06 May 2008, 11:37
puma wrote:
If the sequence x1, x2,x3,...,xn is such that X1=3 and Xn+1 = 2Xn - 1 for n=1, then X20-X19=?

a) 2^19
b) 2^20
c) 2^21
d) 2^20 -1
e) 2^21 -1

your post is not very clear..however..here is how i do it..

xn+1=(2xn)-1

x1=3, x2=5, x3=9 x4=17 x5=33

notice the difference btw x^5-x^4=2^4 or 16, x^4-x^3=2^3...

therefore x^20-x^19=2^19

A it is..
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Re: sequence [#permalink]  06 May 2008, 12:02
puma wrote:
If the sequence x1, x2,x3,...,xn is such that X1=3 and Xn+1 = 2Xn - 1 for n=1, then X20-X19=?

a) 2^19
b) 2^20
c) 2^21
d) 2^20 -1
e) 2^21 -1

X1 = 3 = 2^1 + 1
X2 = 5 = 2^2 + 1
X3 = 9 = 2^3 + 1

This means
x19 = 2^19 + 1
X20 = 2^20 + 1
X20 - X19 = 2^20 + 1 - 2^19 - 1 = 2^20 - 2^19 = 2^19*(2-1) = 2^19
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Re: sequence [#permalink]  07 May 2008, 04:37
I got A

X2=2X1 -1=5=2^2+1

x3=2x2-1=10-1=2^3+1
...

x20-x19= 2x19-1-x19=x19-1

but x19=2^19+1

thus x19-1= 2^19+1-1=2^19
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Re: sequence   [#permalink] 07 May 2008, 04:37
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