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

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New post 19 Dec 2012, 05:35
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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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New post 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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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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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]

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New post 28 Jul 2017, 16:16
If you have the OG 2017: No! you are not crazy it actually says the formula is used for all n>=2n. And on the answer choices it says n>= 2.

This made me take more than 10 minutes to solve because it just did not make sense. Cause if its n>= 2n that means that n = negative integer. BUT we don't have negative integers, so.... wthk am I supposed to do?

JUST WANTED TO LET YOU ALL KNOW! HUGEEEEE MISTAKE ON OG.
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In a certain sequence, the term xn is given by the formula [#permalink]

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New post 28 Dec 2017, 09:17
Bunuel wrote:
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.


Hello Bunuel, i always get confused with such long and weired formulas.

A few questions: How do you call mathematecally n-1 and n-2 written as subscript ? and another question how did you figure out that n-1 is 2 and n-2 is 3 when plugging in ? thank you :)
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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 Dec 2017, 09:23
dave13 wrote:
Bunuel wrote:
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.


Hello Bunuel, i always get confused with such long and weired formulas.

A few questions: How do you call mathematecally n-1 and n-2 written as subscript ? and another question how did you figure out that n-1 is 2 and n-2 is 3 when plugging in ? thank you :)


\(x_n=2*x_{n-1}-\frac{1}{2}*x_{n-2}\) is a formula giving nth term in terms of (n-1)st and (n-2)nd terms. For example, it allows to find say, 3rd term if you know 3-1=2nd and 3-2=1st terms.
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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 Dec 2017, 10:38
Bunuel thanks! A few more questions if you dont mind :)

What does for all n≥2 mean ?
Yes, you marked these in yellow x0=3 and x1=2
x0=3 this expression means that the zero term is 3 and x1=2 means that the first term is 2 correct?
If we need to find 3rd term isn’t it enough to know 2nd term ?
When you solve for x2, where from did you get 3 ?
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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 Dec 2017, 10:50
1
dave13 wrote:
Bunuel thanks! A few more questions if you dont mind :)

What does for all n≥2 mean ?
Yes, you marked these in yellow x0=3 and x1=2
x0=3 this expression means that the zero term is 3 and x1=2 means that the first term is 2 correct?
If we need to find 3rd term isn’t it enough to know 2nd term ?
When you solve for x2, where from did you get 3 ?


1. It means that you can apply the given formula to calculate any term starting from x2;
2. Yes.
3. To get x3 you need x2 and x1 because the formula links nth term to TWO proceeding terms, (n-1)st and (n-2)nd

12. Sequences



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Resources:
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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 xn is given by the formula   [#permalink] 28 Dec 2017, 10:50
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