A sequence of numbers (geometric sequence) is given by the

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A sequence of numbers (geometric sequence) is given by the [#permalink]

19 Jan 2013, 11:53

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A sequence of numbers (geometric sequence) is given by the expression: g(n)=5 *(-1/2)^n. If the sequence begins with n = 1, what are the first two terms for which |g(n) - g(n+1)| < 1/1000 ?

A. g(10), g(11)
B. g(11), g(12)
C. g(12), g(13)
D. g(13), g(14)
E. g(14), g(15)

[Reveal] Spoiler: OA

Last edited by Bunuel on 19 Jan 2013, 12:02, edited 1 time in total.

Edited the question and added OA.

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Re: A sequence of numbers (geometric sequence) is given by the [#permalink]

19 Jan 2013, 12:17

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maglian wrote:

|g(n) - g(n+1)| =|5 *(-\frac{1}{2})^n-5 *(-\frac{1}{2})^{n+1}| --> factor out 5 *(-\frac{1}{2})^n:

|5 *(-\frac{1}{2})^n-5 *(-\frac{1}{2})^{n+1}|=|5 *(-\frac{1}{2})^n*(1-(-\frac{1}{2})^1)|=|5 *(-\frac{1}{2})^n*\frac{3}{2}|=\frac{15}{2}*(\frac{1}{2})^n.

So, we need to find the least value of n for which \frac{15}{2}*(\frac{1}{2})^n<\frac{1}{1000} --> 2^n>7500 --> the least n for which this inequality hods true is 13 (2^13=~8000>7500).

Thus, the first two terms, g(n) and g(n+1), for which the given inequality holds true are g(13) and g(14).

Answer: D.
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Re: A sequence of numbers (geometric sequence) is given by the [#permalink]

19 Jan 2013, 12:23

Bunuel wrote:

So, we need to find the least value of n for which \frac{15}{2}*(\frac{1}{2})^n<\frac{1}{1000} --> 2^n>7500 --> the least n for which this inequality hods true is 13 (2^13=~8000>7500).

Thus, the first two terms, g(n) and g(n+1), for which the given inequality holds true are g(13) and g(14).

Answer: D.

thank you. very simple explanation. you rock.

Re: A sequence of numbers (geometric sequence) is given by the [#permalink] 19 Jan 2013, 12:23

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A sequence of numbers (geometric sequence) is given by the

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A sequence of numbers (geometric sequence) is given by the

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