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# If the sequence x1, x2, x3, , xn, is such that x1 = 3 and

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If the sequence x1, x2, x3, , xn, is such that x1 = 3 and [#permalink]  25 Mar 2006, 13:50
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If the sequence x1, x2, x3, â€¦, xn, â€¦ is such that x1 = 3 and xn+1 = 2xn â€“ 1 for n = 1, then x20 â€“ x19 =
A. 219
B. 220
C. 221
D. 220 - 1
E. 221 - 1

I had trouble setting up the sequence formula, can anyone help?

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Re: PS-sequence [#permalink]  25 Mar 2006, 15:22
Well the answer seems to be 2^19 and A (although your A states 219).
Just write down the first elements and compute the differences.

x1=3
x2=5
x3=9
x4=17

So
x2=x1+2^1
x3=x2+2^2
x4=x3+2^3
... and
x20=x19+2^19, so

x20-x19=2^19.
Re: PS-sequence   [#permalink] 25 Mar 2006, 15:22
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