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GMAT prep - Sequences & Series

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akay: Senior | Next Rank: 100 Posts; Posts: 53; Joined: Sun May 06, 2007 5:03 am

by akay » Fri Aug 10, 2007 5:58 am

Please help with this...

In a certain sequence, the term xn is given by the formula xn=2xn-1 – ½ (xn-2) for all n > 2. If x0=3 and x1=2, what is the value of x3 ?

(A) 2.5
(B) 3.125
(C) 4
(D) 5
(E) 6.75

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Source: Beat The GMAT — Problem Solving | Fri Aug 10, 2007 5:58 am

gabriel: Legendary Member; Posts: 986; Joined: Wed Dec 20, 2006 11:07 amFollowed by: 1 member; Location: India; Thanked: 51 times

Re: GMAT prep - Sequences & Series

by gabriel » Fri Aug 10, 2007 8:00 am

akay wrote:Please help with this...

In a certain sequence, the term xn is given by the formula xn=2xn-1 – ½ (xn-2) for all n > 2. If x0=3 and x1=2, what is the value of x3 ?

(A) 2.5
(B) 3.125
(C) 4
(D) 5
(E) 6.75

well the formula is not very clear ... i am guessing it is X(n)=2*X(n-1)-1/2*X(n-2) ..

we have X(0)=3 and X(1)= 2 ..

we need X(2) ... so substitute n = 2 in the formula .. and we have X(2) = 2 *X(2-1)-1/2*X(2-2) = 2*X(1)-1/2*X(0).. substituting the value of X(1) and X(0) .. in the formula, we get X(2)=2*2-1/2*3 = 4 - 1.5 = 2.5 ..

for finding X(3) .. substitute n = 3 in the formula and we have X(3)= 2*X(2)-1/2*X(1) = 2*2.5- 1/2*2 = 5 - 1 = 4 ... so the answer is C ..

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akay: Senior | Next Rank: 100 Posts; Posts: 53; Joined: Sun May 06, 2007 5:03 am

Re: GMAT prep - Sequences & Series

by akay » Sat Aug 11, 2007 9:04 pm

Spot on Gabriel. My apologies for not making the question easier to read. Appreciate it.

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