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

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19 Dec 2012, 05:35
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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

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:

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

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

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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04 Jun 2013, 05:54
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

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

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05 Jun 2013, 07:35
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
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Re: In a certain sequence, the term xn is given by the formula [#permalink]

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11 Jul 2014, 18:34
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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

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28 Sep 2015, 17:55
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
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Re: In a certain sequence, the term xn is given by the formula [#permalink]

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23 Jun 2016, 09:30
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

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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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