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

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Manager
Joined: 26 Mar 2008
Posts: 99

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

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27 Sep 2008, 12:52
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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?

OA 3?????

Kudos [?]: 251 [0], given: 0

Senior Manager
Joined: 09 Oct 2007
Posts: 463

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27 Sep 2008, 14:08
a4 = 2(a3)-x = 2(27)-x = 54-x
Thus, a5 = 2(a4)-x
108-3x = 99
9/3 = x = 3

Kudos [?]: 54 [0], given: 1

VP
Joined: 05 Jul 2008
Posts: 1402

Kudos [?]: 439 [0], given: 1

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27 Sep 2008, 14:13
arorag 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?

OA 3?????

a5 = 2a4 -x = 4a3-3x = 8a2-7x =99

a3 = 2a2 -x =27 -> 2a2 = 27+x

8a2 = 4 (2a2)

4(27+x) -7x =99

solve for x =3

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Manager
Joined: 27 Sep 2008
Posts: 76

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27 Sep 2008, 14:16
you are missing a ()

a3 = 27
a4 = 2(a3)-x = 2*(27)-x = 54-x
a5 = 2*(54-x)-x = 99

99 = 108-2x-x = 108-3x

x = 3

Kudos [?]: 9 [0], given: 0

Re: PS: sequence   [#permalink] 27 Sep 2008, 14:16
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