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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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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

Originally posted by toyo on 20 Dec 2009, 11:58.
Last edited by Bunuel on 14 Dec 2017, 01:11, 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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New post 20 Dec 2009, 13:23
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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New post 20 Dec 2009, 21:39
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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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New post 20 Dec 2009, 23:48
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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New post 28 Nov 2010, 11:01
can someone give an alternate solution

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

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New post 28 Nov 2010, 11:21
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hirendhanak wrote:
can someone give an alternate solution

thanks in advance


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

Answer: C.

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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New post 28 Nov 2010, 19:01
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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New post 28 Nov 2010, 19:17
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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New post 28 Nov 2010, 19:27
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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New post 28 Nov 2010, 23:35
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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New post 14 Dec 2017, 01:11
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
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: In a certain sequence, the term x_n is given by the formula   [#permalink] 14 Dec 2017, 01:11
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