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If the sequence x1, x2, x3, ... xn, ... is such that x1 = 3 [#permalink]
25 Mar 2006, 13:50

00:00

A

B

C

D

E

Difficulty:

65% (hard)

Question Stats:

70% (03:35) correct
30% (03:36) wrong based on 30 sessions

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 \(n\geq1\), then \(x_{20} - x_{19}\) equals which of the following?

A. 2^19 B. 2^20 C. 2^21 D. (2^20) - 1 E. (2^21) - 1

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.

sorry how did you get x2 =5 and so on? I'm not even understanding the question....x (n+1)=2x(n)-1......isnt this the questions? then how does everything goes into powers of two? Please help!

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.

sorry how did you get x2 =5 and so on? I'm not even understanding the question....x (n+1)=2x(n)-1......isnt this the questions? then how does everything goes into powers of two? Please help!

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 \(n\geq1\), then \(x_{20} - x_{19}\) equals which of the following?

A. 2^19 B. 2^20 C. 2^21 D. (2^20) - 1 E. (2^21) - 1

We have the sequence \(x_1\), \(x_2\), \(x_3\), …, \(x_n,\)… \(x_1=3\) and \(x_{n+1}=2x_n - 1\) for \(n\geq1\).