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# If the infinite sequence a1, a2, a3, ..., an, ..., each term

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Director
Joined: 10 Feb 2006
Posts: 648
If the infinite sequence a1, a2, a3, ..., an, ..., each term  [#permalink]

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Updated on: 25 Mar 2014, 08:48
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81% (00:56) correct 19% (01:28) wrong based on 273 sessions

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In the infinite sequence $$a_1$$, $$a_2$$, $$a_3$$,...., $$a_n$$, each term after the first is equal to twice the previous term. If $$a_5-a_2=12$$, what is the value of $$a_1$$?

A. 4
C. 2
D. 12/7
E. 6/7

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

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-the-infinite-sequence-a1-a2-a3-an-each-term-134617.html

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Originally posted by alimad on 16 May 2008, 03:50.
Last edited by Bunuel on 25 Mar 2014, 08:48, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
Manager
Joined: 27 Jul 2007
Posts: 103

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16 May 2008, 05:46
Is it 6/7 ?
the seq wil be x , 2x, 4x, 8x...........not x^2,x^4 etc
Manager
Joined: 11 Apr 2008
Posts: 147
Schools: Kellogg(A), Wharton(W), Columbia(D)

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16 May 2008, 05:51
1
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
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Joined: 29 Mar 2007
Posts: 2489

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16 May 2008, 07:17
2
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
SVP
Joined: 29 Mar 2007
Posts: 2489

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16 May 2008, 07:18
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
Joined: 23 Sep 2007
Posts: 761

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16 May 2008, 19:00
1
The OA is 6/7
Attachments

infinitesequence.JPG [ 16.16 KiB | Viewed 8226 times ]

Intern
Joined: 20 Feb 2014
Posts: 3
Re: In the infinite sequence, a1,a2,a3,,,,an, each term after  [#permalink]

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25 Mar 2014, 07:49
a5=2^4*x
a2=2^1*x

So a5-a2=16x-12x=14x
14x=12 => x=6/7
Math Expert
Joined: 02 Sep 2009
Posts: 47206
Re: If the infinite sequence a1, a2, a3, ..., an, ..., each term  [#permalink]

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25 Mar 2014, 08:46
In the infinite sequence $$a_1$$, $$a_2$$, $$a_3$$,...., $$a_n$$, each term after the first is equal to twice the previous term. If $$a_5-a_2=12$$, what is the value of $$a_1$$?

A. 4
C. 2
D. 12/7
E. 6/7

The formula for calculating $$n_{th}$$ term would be $$a_n=2^{n-1}*a_1$$ . So:
$$a_5=2^4*a_1$$;
$$a_2=2*a_1$$;

Given: $$a_5-a_2=2^4*a_1-2*a_1=12$$ --> $$2^4*a_1-2*a_1=12$$ --> $$a_1=\frac{12}{14}=\frac{6}{7}$$.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-the-infinite-sequence-a1-a2-a3-an-each-term-134617.html
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Senior Manager
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Posts: 251
Re: If the infinite sequence a1, a2, a3, ..., an, ..., each term  [#permalink]

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30 Aug 2017, 11:27
Process elimination could work as well.

a5 - a2
96/7 - 12/7
12
Target Test Prep Representative
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Posts: 2679
Re: If the infinite sequence a1, a2, a3, ..., an, ..., each term  [#permalink]

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02 Sep 2017, 07:08
In the infinite sequence $$a_1$$, $$a_2$$, $$a_3$$,...., $$a_n$$, each term after the first is equal to twice the previous term. If $$a_5-a_2=12$$, what is the value of $$a_1$$?

A. 4
C. 2
D. 12/7
E. 6/7

We can let a_1 = x, a_2 = 2x, a_3 = 4x, a_4 = 8x and a_5 = 16x. Thus:

16x - 2x = 12

14x = 12

x = 12/14 = 6/7

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Re: If the infinite sequence a1, a2, a3, ..., an, ..., each term &nbs [#permalink] 02 Sep 2017, 07:08
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