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

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Intern
Joined: 22 Sep 2007
Posts: 32

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In the infinite sequence a1, a2, a3.....an, each term after [#permalink]

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04 Jan 2008, 05:07
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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?

a)4
c) 2
d) 12/7
e) 6/7

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CEO
Joined: 17 Nov 2007
Posts: 3583

Kudos [?]: 4672 [0], given: 360

Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Re: Number Sequence [#permalink]

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04 Jan 2008, 06:14
E

a1
a2=a1*2
a3=a1*2^2
...
an=a1*2^(n-1)
...

a5-a2=12 ==> a1*2^4-a1*2^1=12 ==> a1=12/(16-2)=6/7
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Kudos [?]: 4672 [0], given: 360

Manager
Joined: 01 Jan 2008
Posts: 222

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Schools: Booth, Stern, Haas
Re: Number Sequence [#permalink]

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04 Jan 2008, 06:17
I even don't know what to say

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Director
Joined: 12 Jul 2007
Posts: 857

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Re: Number Sequence [#permalink]

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04 Jan 2008, 08:00
kazakhb wrote:
I even don't know what to say

Let's simplify this question:

The pattern says that each term is equal to twice previous term so:

Let A1 = X
Let A2 = 2x
Let A3 = 4x
Let A4 = 8x
Let A5 = 16x

or

A1 = X
A2 = 2x
A3 = 2^2(x)
A4 = 2^3(x)
A5 = 2^4(x)

(if this were a problem that involved much larger values, say A32 and A28 it would be beneficial to see this pattern as Ax = 2^(x-1)x as shown above. however, if we're dealing with A5 and A2 we can think of it the first way because it's the easiest approach)

Now that we have the values for A5 and A2 we can set up a formula and solve for x (which represents A1)

A5-A2 = 16x-2x = 12
14x = 12
x = 12/14 = 6/7

and BAM! You're finished and that's all there is to it!

You'll have to forgive Walker. He's a certified math god and operates on a higher plane of quant logic than anyone I've seen . Walker can create an simply elegant formula for any problem you throw at him and solve it accurately.

Kudos [?]: 334 [0], given: 0

CEO
Joined: 17 Nov 2007
Posts: 3583

Kudos [?]: 4672 [0], given: 360

Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Re: Number Sequence [#permalink]

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04 Jan 2008, 08:17
eschn3am wrote:
...and operates on a higher plane of quant logic than anyone....

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Kudos [?]: 4672 [0], given: 360

Re: Number Sequence   [#permalink] 04 Jan 2008, 08:17
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# In the infinite sequence a1, a2, a3.....an, each term after

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