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The sequence a1, a2, … , a n, … is such that an = 2an-1 - x [#permalink]

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04 Jun 2007, 20:23

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The sequence \(a_1\), \(a_2\), … , \(a_n\), … is such that \(a_n = 2a_{n-1} - x\) for all positive integers n ≥ 2 and for certain number x. If \(a_5 = 99\) and \(a_3 = 27\), what is the value of x?

Q13: The sequence a1, a2, … , a n, … is such that an = 2an-1 - x for all positive integers n ≥ 2 and for certain number x. If a5 = 99 and a3 = 27, what is the value of x?

The sequence a1, a2, … , a n, … is such that an = 2an-1 - x for all positive integers n ≥ 2 and for certain number x. If a5 = 99 and a3 = 27, what is the value of x? A. 3 B. 9 C. 18 D. 36 E.45

Quite simple to solve this one.

Given: \(a_n = 2a_{n-1} - x\)

\(a_5 = 99\)

\(a_3 = 27\)

\(a_5 = 2a_4 - x = 2(2a_3 - x) - x = 4a_3 - 3x = 99\)

The sequence a1…..a2.......an........is such that an=2an-1-X for all positive integers n>=2 and for certain number X. If a5=99 and a3=27, what is the value of X?
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The sequence a1…..a2.......an........is such that an=2an-1-X for all positive integers n>=2 and for certain number X. If a5=99 and a3=27, what is the value of X?

Plug the known values a5=99 and a3 = 27 into the formula:

a5 = 2(a4) - x 99 = 2(a4) - x

a4 = 2(a3) - x a4 = 2(27)-x = 54-x

Substitute 54-x for a4 in the top equation: 99 = 2(54-x)-x 99=108-3x 3x=9 x=3

On the GMAT, I would recommend that you plug in the answer choices, one of which would say that x=3.

Plug a5 = 99 and x=3 into the formula: 99 = 2(a4) -3 a4 = 51

Plug a4=51, a3=27, and x=3 into the formula: 51 = 2(27) - 3 51 = 51. Success!
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The sequence a1…..a2.......an........is such that an=2an-1-X for all positive integers n>=2 and for certain number X. If a5=99 and a3=27, what is the value of X?

A5=99 and A3=27 According to the given nth term, A5=2(A4)-x=2{2(A3)-x}-x=2{(2*27)-x}-x=108-2x-x=108-3x Hence 108-3x=99 or x=9/3=3

Re: Q13: The sequence a1, a2, , a n, is such that an = 2an-1 [#permalink]

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23 Dec 2013, 11:58

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: The sequence a1, a2, … , a n, … is such that an = 2an-1 - x [#permalink]

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04 Jul 2014, 08:51

whiplash2411 wrote:

udaymathapati wrote:

The sequence a1, a2, … , a n, … is such that an = 2an-1 - x for all positive integers n ≥ 2 and for certain number x. If a5 = 99 and a3 = 27, what is the value of x? A. 3 B. 9 C. 18 D. 36 E.45

Quite simple to solve this one.

Given: \(a_n = 2a_{n-1} - x\)

\(a_5 = 99\)

\(a_3 = 27\)

\(a_5 = 2a_4 - x = 2(2a_3 - x) - x = 4a_3 - 3x = 99\)

\(4(27) - 3x = 99\)\(3x = 108-99 = 9\)

\(x = 3\)

QUESTION : How exactly did you get from 2(2a3 - x) to 4a3 * 3x, wouldn't it be 4a3 - 2x?

The sequence a1, a2, … , a n, … is such that an = 2an-1 - x for all positive integers n ≥ 2 and for certain number x. If a5 = 99 and a3 = 27, what is the value of x? A. 3 B. 9 C. 18 D. 36 E.45

Quite simple to solve this one.

Given: \(a_n = 2a_{n-1} - x\)

\(a_5 = 99\)

\(a_3 = 27\)

\(a_5 = 2a_4 - x = 2(2a_3 - x) - x = 4a_3 - 3x = 99\)

\(4(27) - 3x = 99\)\(3x = 108-99 = 9\)

\(x = 3\)

QUESTION : How exactly did you get from 2(2a3 - x) to 4a3 * 3x, wouldn't it be 4a3 - 2x?

Re: The sequence a1, a2, … , a n, … is such that an = 2an-1 - x [#permalink]

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23 Nov 2016, 09:20

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
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Re: The sequence a1, a2, … , a n, … is such that an = 2an-1 - x [#permalink]

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21 Jan 2017, 03:28

jet1445 wrote:

The sequence \(a_1\), \(a_2\), … , \(a_n\), … is such that \(a_n = 2a_{n-1} - x\) for all positive integers n ≥ 2 and for certain number x. If \(a_5 = 99\) and \(a_3 = 27\), what is the value of x?