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if x1, x2, x3......xn is such that x1 = 3 and xn+1 = 2.xn-1 [#permalink]
 06 Sep 2004, 17:32
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if x1, x2, x3......xn is such that x1 = 3 and xn+1 = 2.xn-1 for all n >= 1 then x20-x19 =
1. 2^19
2. 2^20
3. 2^21
4. 2^20-1
5. 2^21-1
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Director
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X20=2X19-1
X19=2X18-1
-> X20-X19=2(X19-X18) .... recursive relation
or X20-X19=2^18(X2-X1)=2^19
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Manager
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srijay your answer is correct.
i followed your steps all the way till the end but did not get how x2-x1 = 2
please let me know how you did that part
thanks
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Director
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srijay007 wrote: X20=2X19-1
X19=2X18-1
-> X20-X19=2(X19-X18) .... recursive relation
or X20-X19=2^18(X2-X1)=2^19
X20-X19
=2(X19-X18)
=2*2(X18-X17)
.
.
.
=2^(19-2+1)*(X2-X1)
This is what I did
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Manager
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yep i got that part.. just wondering how you wetn from 2^18(x2-x1) to 2^19
i.e. x2-x1 = 2
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Director
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damit wrote: srijay your answer is correct.
i followed your steps all the way till the end but did not get how x2-x1 = 2
please let me know how you did that part
thanks
oh misread ur question
I solved x2=2*x1-1=5
x1 is given as 3
hence x2-x1=2
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GMAT Club Legend
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What does the Xn-1 mean? Are they all in subcript, meaning,
if n =1, Xn-1 = 19
or is n the subscript meaning,
if n = 10, Xn-1 = X10 - 1
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GMAT Club Legend
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n=19, Xn+1 = X20 = 2(X19-1) = 2(X18)
n=18, Xn+1 = X19 = 2(X18-1) = 2(X17)
So X20-X19 = 2(X18) - 2(X17) = 2(X18-X17)
X18 = 2(X16)
X17 = 2(X15)
So X20-X19 = 2^2(X16-X15)
So if we keep reducing it, we should eventually end up with
2^9(X2-X0)
I can't seem to get further than this.
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Director
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srijay007 wrote: ywilfred wrote: What does the Xn-1 mean? Are they all in subcript, meaning,
if n =1, Xn-1 = 19
or is n the subscript meaning,
if n = 10, Xn-1 = X10 - 1 Ya it's subscript if n=10 Xn-1 means X9 No, I think they are not all subscripts. xn+1 = 2.xn-1 means xn+1 = (2.xn) - 1
My soln:
I solved till n=4, then generalised the sequence.
n1=3, n2=5, n3=9, n4=17..., (2^n+1)+1
Therefore: x20-x19
= 2(X19) - 1 - (X19)
= X19 - 1
= 2^19 + 1 -1
= 2^19
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Manager
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my 2 cents: ans - A- 2^19
x1 = 3
x2 = 5 - diff = 2
x3 = 8 - diff = 4
x4 = 17 - diff = 8
x5 = 33 - diff = 16
and so on
so the difference between consecutive terms follows the sequence
Xn - Xn-1 = 2^(n-1)
so X20 - X19 = 2^19
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