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In a certain sequence, the term xn is given by the formula

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In a certain sequence, the term xn is given by the formula [#permalink] New post 19 Dec 2012, 05:33
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In a certain sequence, the term x_n is given by the formula x_n=2*x_{n-1}-\frac{1}{2}*x_{n-2} for all n\geq{2}. If x_0=3 and x_1=2, what is the value of x_3?

(A) 2.5
(B) 3.125
(C) 4
(D) 5
(E) 6.75
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Re: In a certain sequence, the term xn is given by the formula [#permalink] New post 19 Dec 2012, 05:35
Walkabout wrote:
In a certain sequence, the term x_n is given by the formula x_n=2*x_{n-1}-\frac{1}{2}*x_{n-2} for all n\geq{2}. If x_0=3 and x_1=2, what is the value of x_3?

(A) 2.5
(B) 3.125
(C) 4
(D) 5
(E) 6.75


We have a formula to calculate the value of the terms in the sequence starting from x_2: x_n=2*x_{n-1}-\frac{1}{2}*x_{n-2}. Hence:

x_2=2*x_{1}-\frac{1}{2}*x_{0}=2*2-\frac{1}{2}*3=\frac{5}{2};

x_3=2*x_{2}-\frac{1}{2}*x_{1}=2*\frac{5}{2}-\frac{1}{2}*2=4.

Answer: C.

Hope it's clear.
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Re: In a certain sequence, the term xn is given by the formula   [#permalink] 19 Dec 2012, 05:35
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