In a certain sequence, the term xn is given by the formula

Question

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

PS16100

Bunuel · Accepted Answer

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.

avigutman · Answer

Video solution from Quant Reasoning: Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1 https://www.youtube.com/watch?v=1eR-2ybv6Fs

Bunuel · Answer

Bumping for review and further discussion*. Get a kudos point for an    alternative    solution!

*New project from GMAT Club!!! Check  HERE

ziko · Answer

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

ScottTargetTestPrep · Answer

(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.

valepm · Answer

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.

dave13 · Answer

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

Bunuel · Answer

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.

dave13 · Answer

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 ?

Bunuel · Answer

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 
     Theory   
 Math : Sequences & Progressions 
     Questions   
 Special Numbers and Sequences Problems 
 DS Questions 
 PS Questions

JDF · Answer

The timer says 88% of people got it right but I bet I can count on my fingers the number who did it in two minutes.

Posted from my mobile device

woohoo921 · Answer

ScottTargetTestPrep I approached this problem by brute force if you will in that I started by plugging in 3 to X (so x sub 3) to see what I was missing. Is this a bad approach to use when solving other recursive formulas? Thank you

bagad.07 · Answer

OG Question Code: PS16100

Bunuel · Answer

________________________________
Thank you! Added to the first post.

bumpbot · Answer

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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

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