Problem Solving

If the sequence x<1>, x<2>,.....x<n>, is such that x<1> = 3 and x<n+1> = 2x<n>-1 for n greater than or equal to 1, then x<20>-x<19>=

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

Thanks

not a clue

The correct answer should be [spoiler]2^19[/spoiler]. Let me explain:

We'll do this by pattern recognition.

We are told that X(1)=3

Also we are given that X(n+1)=2X(n)-1

Let's find the first few terms.
X(2) = 2*X(1)-1 = 2*3-1 = 5
X(3) = 2*X(2)-1 = 2*5-1 = 9
X(4) = 2*X(3)-1= 2*9-1 = 17

We need to find X(20)-X(19)

Observe the pattern
X(2)-X(1) = 5-3 = 2 = 2^1
X(3)-X(2) = 9 - 5= 4 = 2^2.
X(4)-X(3) = 17-9 = 8 = 2^3.
So X(20)-X(19) must be 2^19.
Hence A is the answer.
Let me know if this helps

yeah.. i too got the answer. it is very straight, however,there is a clause in the question stating, for all n less than or equal to 1 ..

How is this not considered while answering the question.?
because if this condition is true, then we will not be getting any value after x<2>.

So what about it ?

Its a transcription error. I saw it when i solved it and figured that it must read "n is greater than or equal to 1."

eagleeye wrote:Its a transcription error. I saw it when i solved it and figured that it must read "n is greater than or equal to 1."

I fixed the error, sorry about that. Thanks again for showing how to solve it.