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Manager
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If the sequence x1, x2,x3,...,xn is such that X1=3 and Xn+1 [#permalink]
 06 May 2008, 12:05
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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Current Student
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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 therefore the answer is A 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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Senior Manager
Joined: 20 Feb 2008
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Location: Bangalore, India
Schools: R1:Cornell, Yale, NYU. R2: Haas, MIT, Ross
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My answer is A 2^19
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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Current Student
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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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VP
Joined: 10 Jun 2007
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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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Director
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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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