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In a certain sequence, the (OG16)

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by boomgoesthegmat » Thu May 19, 2016 3:47 pm

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Difficulty—

In a certain sequence, the term x(n) is given by the formula x(n) = 2xn(n-1) - (1/2)(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

OA: C
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by OptimusPrep » Thu May 19, 2016 7:49 pm
boomgoesthegmat wrote:In a certain sequence, the term x(n) is given by the formula x(n) = 2xn(n-1) - (1/2)(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

OA: C
Hi boomgoesthegmat,
Can you please re check the question prompt. I feel there is a problem with the term " 2xn(n-1)"
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by Jeff@TargetTestPrep » Thu Jun 28, 2018 5:12 pm
boomgoesthegmat wrote:In a certain sequence, the term x(n) is given by the formula x(n) = 2xn(n-1) - (1/2)(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
We see that

x(2) = 2(2) - (1/2)(3) = 4 - 1.5 = 2.5

So

x(3) = 2(2.5) - (1/2)(2) = 5 - 1 = 4

Answer: C

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