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# In a certain sequence, the term x_n is given by the formula

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In a certain sequence, the term x_n is given by the formula [#permalink]

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20 Dec 2009, 10:58
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Question Stats:

84% (01:30) correct 16% (01:43) wrong based on 80 sessions

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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

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/in-a-certain ... 44376.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 14 Dec 2017, 00:11, edited 2 times in total.
Edited the question and added the OA.

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

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20 Dec 2009, 12:23
toyo wrote:
In a certain sequence, the term xn is given by the formula x^n=2x^n-1 – ½ (x^n-2) for all n > 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

The answer is 4, does anyone know how to solve this problem?

First step is to solve for x^2

x^n-1 is the previous term or x^1 which is 2
x^-2 is the 2nd previous term or X^0 which is 3

2(2) - 1/2(3)
4 - (3/2) = 5/2
so x^2 = 5/2

Now to find x^3
Using the same logic from above
x^n-1 previous term or x^2 which is equal to 5/2
n^n-2 2nd previous term or x^1 which is equal to 2
2(5/2) - 1/2(2)
5-1 = 4

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

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20 Dec 2009, 20:39
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First find X2 using X0 & X1
Then find X3 using X1 & X2.

4 is the answer you will get.
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Re: In a certain sequence, the term x_n is given by the formula [#permalink]

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20 Dec 2009, 22:48
X^N=2(X^(n-1))-1/2(X^(n-2))

-->X^2=2X^1-1/2(X^0)=2*2-1/2 * 3=5/2

PUT X^1,X^2 IN X^3

ANS WILL BE 4
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Re: In a certain sequence, the term x_n is given by the formula [#permalink]

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28 Nov 2010, 10:01
can someone give an alternate solution

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

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28 Nov 2010, 10:21
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Expert's post
hirendhanak wrote:
can someone give an alternate solution

The original question is as follows:
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

So we have a formula to calculate the value of the terms in the sequence starting from $$x_2$$:
$$x_n=2*x_{n-1}-\frac{1}{2}*x_{n-2}$$. So, $$x_2=2*x_{1}-\frac{1}{2}*x_{0}=2*2-\frac{1}{2}*3=\frac{5}{2}$$;

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

Hope it's clear.
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Re: In a certain sequence, the term x_n is given by the formula [#permalink]

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28 Nov 2010, 18:01
How can x^0=3 I thought this would equal 1 no matter the integer?

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

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28 Nov 2010, 18:17
gettinit wrote:
How can x^0=3 I thought this would equal 1 no matter the integer?

It is not $$x^0$$. Actually it is $$x_0=3$$.
(All $$x^n$$ are actually $$x_n$$)

It is like a function f(n) where they have asked you f(3) and given you f(0) and f(1). You use f(0) and f(1) to get f(2) and then you use f(1) and f(2) to get f(3).
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Re: In a certain sequence, the term x_n is given by the formula [#permalink]

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28 Nov 2010, 18:27
VeritasPrepKarishma wrote:
gettinit wrote:
How can x^0=3 I thought this would equal 1 no matter the integer?

It is not $$x^0$$. Actually it is $$x_0=3$$.
(All $$x^n$$ are actually $$x_n$$)

It is like a function f(n) where they have asked you f(3) and given you f(0) and f(1). You use f(0) and f(1) to get f(2) and then you use f(1) and f(2) to get f(3).

Thanks Karishma I was lost in the notation - very confusing the way the problem was written.

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

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28 Nov 2010, 22:35
plug and play and answer should be 4

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

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14 Dec 2017, 00:11
toyo 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

OPEN DISCUSSION OF THIS QUESTION IS HERE: https://gmatclub.com/forum/in-a-certain ... 44376.html
_________________

Kudos [?]: 139512 [0], given: 12794

Re: In a certain sequence, the term x_n is given by the formula   [#permalink] 14 Dec 2017, 00:11
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# In a certain sequence, the term x_n is given by the formula

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