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The sequence a1, a2, … , a n, … is such that an = 2an1  x [#permalink]
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04 Jun 2007, 19:23
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The sequence \(a_1\), \(a_2\), … , \(a_n\), … is such that \(a_n = 2a_{n1}  x\) 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? A. 3 B. 9 C. 18 D. 36 E. 45
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Last edited by Bunuel on 24 Dec 2013, 00:16, edited 1 time in total.
Renamed the topic, edited the question and added the OA.



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Re: PS  Sequence (a1, a2, …) [#permalink]
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05 Jun 2007, 01:37
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jet1445 wrote: Q13: The sequence a1, a2, … , a n, … is such that an = 2an1  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
a5= 2*a4  x = 99
a4 = 2*a3  x = 2*27  x
therefore;
a5 = 2*(54  x ) x = 99
108  3*x = 99
therefore X = 3
This the answer is "A"



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Re: Sequence Problem [#permalink]
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28 Aug 2010, 06:30
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Good one. Please let me know if some one comes up with a solution that can be worked under 2 mins given an= 2an1  x a5 = 99 = 2 a4  X = 2[2a3X] X = 4 a3  3X given a3 = 27 ; substituting: 108  3X = 99 => X = 3 A



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Re: Sequence Problem [#permalink]
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28 Aug 2010, 09:13
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udaymathapati wrote: The sequence a1, a2, … , a n, … is such that an = 2an1  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: \(a_n = 2a_{n1}  x\) \(a_5 = 99\) \(a_3 = 27\) \(a_5 = 2a_4  x = 2(2a_3  x)  x = 4a_3  3x = 99\) \(4(27)  3x = 99\)\(3x = 10899 = 9\) \(x = 3\)



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Sequence [#permalink]
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20 Oct 2010, 05:25
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The sequence a1….. a2....... an........is such that an= 2an1X 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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Re: Sequence [#permalink]
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20 Oct 2010, 05:50
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monirjewel wrote: The sequence a1…..a2.......an........is such that an=2an1X 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 = 54x Substitute 54x for a4 in the top equation: 99 = 2(54x)x 99=1083x 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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Re: Sequence [#permalink]
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20 Oct 2010, 05:56
monirjewel wrote: The sequence a1…..a2.......an........is such that an=2an1X 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=1082xx=1083x Hence 1083x=99 or x=9/3=3 Consider KUDOS if its helpful.



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Re: PS  Sequence (a1, a2, …) [#permalink]
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11 Sep 2011, 09:03
a(n) = 2*a(n1) x
a5 = 99 a3=27
a5 = 2a4x a4 = 2a3x
=>99 = 2(2a3x)x
99 = 4a33x = 4*273x
=>x=3
Answer is A.



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Re: PS  Sequence (a1, a2, …) [#permalink]
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12 Sep 2011, 04:14
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A is the answer
a4= 54x
=> a5 = 2 (54 x) x = 99
=> 108  3x = 99 => x= 3



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Re: Q13: The sequence a1, a2, , a n, is such that an = 2an1 [#permalink]
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23 Dec 2013, 10:58
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Re: The sequence a1, a2, … , a n, … is such that an = 2an1  x [#permalink]
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04 Jul 2014, 07:51
whiplash2411 wrote: udaymathapati wrote: The sequence a1, a2, … , a n, … is such that an = 2an1  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: \(a_n = 2a_{n1}  x\) \(a_5 = 99\) \(a_3 = 27\) \(a_5 = 2a_4  x = 2(2a_3  x)  x = 4a_3  3x = 99\) \(4(27)  3x = 99\)\(3x = 10899 = 9\) \(x = 3\) QUESTION : How exactly did you get from 2(2a3  x) to 4a3 * 3x, wouldn't it be 4a3  2x?



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Re: The sequence a1, a2, … , a n, … is such that an = 2an1  x [#permalink]
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04 Jul 2014, 07:59



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Re: The sequence a1, a2, … , a n, … is such that an = 2an1  x [#permalink]
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23 Nov 2016, 08:20
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Re: The sequence a1, a2, … , a n, … is such that an = 2an1  x [#permalink]
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21 Jan 2017, 02:28
jet1445 wrote: The sequence \(a_1\), \(a_2\), … , \(a_n\), … is such that \(a_n = 2a_{n1}  x\) 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?
A. 3 B. 9 C. 18 D. 36 E. 45 \(a_5= 2*a_4  x = 99\) \(a_4 = 2*a_3  x = 2*27  x\) \(a_5 = 2*(54  x ) x = 99\) 108  3*x = 99 Therefore X = 3 Hence option A is correct.



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Re: The sequence a1, a2, … , a n, … is such that an = 2an1  x [#permalink]
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01 Aug 2017, 11:23
I did not understand the relation at first, but giving another shot worked well, thanks. a5=99 a3=27 a5=2a4−x =2(2a3−x)−x =4a3−3x=99a5 =2a4−x =2(2a3−x)−x =4a3−3x=99 4(27)−3x =994(27)−3x =993x =108−99 =93x =108−99 =9 x=3
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