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A special sequence of numbers is written as 2, 9, 28, 65, 12

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A special sequence of numbers is written as 2, 9, 28, 65, 12 [#permalink] New post 22 May 2012, 08:16
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A special sequence of numbers is written as 2, 9, 28, 65, 126 …….Find the ratio of the 7th term to the 15th term.

A. 1/4
B. 1/2
C. 129/422
D. 43/422
E. 43/129

couldn't get the logic behind the terms in the sequence :(
[Reveal] Spoiler: OA
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Re: special sequence of numbers is written as 2, 9, 28, 65 [#permalink] New post 22 May 2012, 08:24
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Sequence is

1^3+1...2^3+1...3^3+1.....7^3+1.....15^3+1

Ratio thus is

\frac{7^3+1}{15^3+1}

Not sure what the quick way to simplify this is...
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Re: A special sequence of numbers is written as 2, 9, 28, 65, 12 [#permalink] New post 24 May 2012, 09:17
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gmihir wrote:
A special sequence of numbers is written as 2, 9, 28, 65, 126 …….Find the ratio of the 7th term to the 15th term.

A. 1/4
B. 1/2
C. 129/422
D. 43/422
E. 43/129

couldn't get the logic behind the terms in the sequence :(


The series as pointed out already is (1^3+1) , (2^3+1) , (3^3+1) , (4^3+1)..
So, ratio of the 7th term to the 15th term = 7^3+1/15^3+1

Simplify it as (7+1)(7^2 - 7*1 + 1)/(15+1)(15^2 - 15*1 + 1)
because a^3 + b^3 = (a+b)(a^2-ab+b^2)

So, our ratio is 8*43/16*211 = 43/422

Answer D.
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Re: A special sequence of numbers is written as 2, 9, 28, 65, 12 [#permalink] New post 30 Dec 2013, 02:06
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Re: special sequence of numbers is written as 2, 9, 28, 65 [#permalink] New post 13 Jan 2014, 09:39
Cares wrote:
Sequence is

1^3+1...2^3+1...3^3+1.....7^3+1.....15^3+1

Ratio thus is

\frac{7^3+1}{15^3+1}

Not sure what the quick way to simplify this is...


Well I'll tel you what I did

You end up with 344/3375

I just used what I call 'Brute Force Heavy discount shorcut' and ended up with 3/33 = 1/11 approx

So among the answer choices the only one that made sence was D

Not sure if there is another approach that might be more elegant

Cheers!
J :)

PS. After reflecting on this...

Actually what one can do is the following:

Once you get to (7/15)^3 then this is approx 1/8

Only answer choice that even comes close to 1/8 is answer choice D

Hence D it is!
Re: special sequence of numbers is written as 2, 9, 28, 65   [#permalink] 13 Jan 2014, 09:39
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A special sequence of numbers is written as 2, 9, 28, 65, 12

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