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In a certain list of numbers, the first number is 2, the second number

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In a certain list of numbers, the first number is 2, the second number [#permalink]

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New post 25 Nov 2012, 23:48
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In a certain list of numbers, the first number is 2, the second number is 3, and each succeeding number is the sum of all the numbers that precede it in the list. If h and k denote the 20th and 24th numbers in the list, respectively, what is the value of k/h ?

A. 5
B. 8
C. 10
D. 16
E. 20
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Re: In a certain list of numbers, the first number is 2, the second number [#permalink]

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New post 26 Nov 2012, 00:13
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The trick here is to notice that:

1] This is actually a disguised Geometric Progression from the 3rd term onwards: 2, 3, 5, 10, 20, 40, 80...
2] Because the Geometric Progression starts from the 3rd term of the set, the nth term in the set is actually the (n-2)th term of the Geometric Progression part of the set

Now armed with these two observation, apply the formula for nth term of any Geometric Progression = b X r^(n-1); remember b is 5 and n will be the 18th and 22nd term respectively, NOT 20th and 24th because of the 2nd observation above.

h = 18th term of the GP = 5 X 2^17
k = 22nd term of the GP = 5 X 2^21

k/h = 2^4 = 16

Therefore D is the correct answer. ;)

Hope this helped.
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Re: In a certain list of numbers, the first number is 2, the second number [#permalink]

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Re: In a certain list of numbers, the first number is 2, the second number [#permalink]

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New post 10 Jan 2017, 09:22
Bunuel could you pls post your solution\
Thanks
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Re: In a certain list of numbers, the first number is 2, the second number [#permalink]

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New post 13 Jan 2017, 08:24
I solved in the following way:

1. Look at the series of first numbers: 2, 3, 5, 10, 20, 40, 80, 160, 320, etc.
2. Starting from the 3rd value (5) the series represents a geometric progression, so the ratio of each number with the previous one remains constant
3. the 20th value can be represented by each value from 5 onward and the 24th value will be after 4 places (e.g. 80/5, 160/10, 320/20 etc.)
4. I every case the ratio will be 16

Hope this is helpful and please let me know if there is something incorrect
Re: In a certain list of numbers, the first number is 2, the second number   [#permalink] 13 Jan 2017, 08:24
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