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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
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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] 28 Sep 2015, 17:55
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