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# In the infinite sequence, a1,a2,a3,,,,an, each term after

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Director
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In the infinite sequence, a1,a2,a3,,,,an, each term after [#permalink]  16 May 2008, 02:50
1
KUDOS
In the infinite sequence, a1,a2,a3,,,,an, each term after the first is equal to twice the previous term. If a5-a2 =12, what is the value of a1?

The sequence looks more like x,x^2,x^4,x^8,x^16

a5 = x^16
a2=x^2

x^16-x^2 = 12
x^2(x^8 -1 ) = 12

I'm lost here. Thanks
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Manager
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Re: Infinite sequence [#permalink]  16 May 2008, 04:46
Is it 6/7 ?
the seq wil be x , 2x, 4x, 8x...........not x^2,x^4 etc
Manager
Joined: 11 Apr 2008
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Schools: Kellogg(A), Wharton(W), Columbia(D)
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Re: Infinite sequence [#permalink]  16 May 2008, 04:51
1
KUDOS
In the infinite sequence, a1,a2,a3,,,,an, each term after the first is equal to twice the previous term. If a5-a2 =12, what is the value of a1?

The sequence looks more like x,x^2,x^4,x^8,x^16

a5 = x^16
a2=x^2

x^16-x^2 = 12
x^2(x^8 -1 ) = 12

I'm lost here. Thanks

The sequence is
x, 2*x, 2*(2*x), 2*(2*(2*x)) .....
i.e.

nth term = 2^(n-1)x

a5=2^4 * x
a2=2^2*x

=> a5-a2 = (16-4)x= 12x
thus, 12x=12
and the first term x=1
CEO
Joined: 29 Mar 2007
Posts: 2596
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Re: Infinite sequence [#permalink]  16 May 2008, 06:17
1
KUDOS
In the infinite sequence, a1,a2,a3,,,,an, each term after the first is equal to twice the previous term. If a5-a2 =12, what is the value of a1?

The sequence looks more like x,x^2,x^4,x^8,x^16

a5 = x^16
a2=x^2

x^16-x^2 = 12
x^2(x^8 -1 ) = 12

I'm lost here. Thanks

x. 2x. 4x. 8x. 16x. 16x-2x=12 14x=12. x=6/7
CEO
Joined: 29 Mar 2007
Posts: 2596
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Kudos [?]: 166 [0], given: 0

Re: Infinite sequence [#permalink]  16 May 2008, 06:18
anirudhoswal wrote:
In the infinite sequence, a1,a2,a3,,,,an, each term after the first is equal to twice the previous term. If a5-a2 =12, what is the value of a1?

The sequence looks more like x,x^2,x^4,x^8,x^16

a5 = x^16
a2=x^2

x^16-x^2 = 12
x^2(x^8 -1 ) = 12

I'm lost here. Thanks

The sequence is
x, 2*x, 2*(2*x), 2*(2*(2*x)) .....
i.e.

nth term = 2^(n-1)x

a5=2^4 * x
a2=2^2*x

=> a5-a2 = (16-4)x= 12x
thus, 12x=12
and the first term x=1

This cannot be correct.

Just try it. 1, 2, 4, 8, 16. 16-2 dsnt = 12.
Director
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Posts: 799
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Re: Infinite sequence [#permalink]  16 May 2008, 18:00
1
KUDOS
The OA is 6/7
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Re: Infinite sequence   [#permalink] 16 May 2008, 18:00
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