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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]

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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]

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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]

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Re: In a certain sequence, the term xn is given by the formula [#permalink]

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New post 05 Jun 2013, 07:35
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



X(3)= 2*X(2)-X(1)/2
X(2)=2X(1)-X(0)/2=2*2-3/2=5/2
X(3)= 2*5/2-2/2=5-1=4 Answer is C
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Re: In a certain sequence, the term xn is given by the formula [#permalink]

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Re: In a certain sequence, the term xn is given by the formula [#permalink]

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New post 28 Sep 2015, 17:55
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Re: In a certain sequence, the term xn is given by the formula [#permalink]

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New post 23 Jun 2016, 09:30
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


(Note that the * symbol in both the question stem and in this solution indicates multiplication.)

We are given that X(n) = 2 * X(n-1) – ½ * X(n-2), for all n=>2. This is called a recursive formula, which means that we need to know prior terms before we can compute the subsequent terms. For example, if we want to know X(2), we must know both X(1) and X(0), because X(2) is equal to 2 * X(1) – ½ * X(0).

We are given X(1) = 2 and X(0) = 3. So, when n is 2, X(2) would be calculated as follows:

X(2) = 2 * X(1) – ½ * X(0)

X(2) = 2 * 2 – ½ * 3

X(2) = 4 – 1.5

X(2) = 2.5

Now we are ready to determine the value of X(3). In this case, n = 3, X(1) is 2, and X(2) is 2.5. We plug these values into the recursive formula given in the question stem:

X(3) = 2 * X(2) – ½ * X(1)

X(3) = 2 * 2.5 – ½ * 2

X(3) = 5 – 1

X(3) = 4

Answer is C.
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Re: In a certain sequence, the term xn is given by the formula   [#permalink] 23 Jun 2016, 09:30
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