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# In a certain sequence, the term [m]A_n[/m] is given

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NUS School Moderator
Joined: 18 Jul 2018
Posts: 982
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
In a certain sequence, the term [m]A_n[/m] is given  [#permalink]

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28 Jan 2019, 20:37
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Difficulty:

65% (hard)

Question Stats:

64% (02:51) correct 36% (03:17) wrong based on 11 sessions

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In a certain sequence, the term $$A_n$$ is given by the formula $$A_n = 16 - \frac{(4-n)^3}{|n-4|}$$ for all positive integers n≠4, While $$A_4 = 16$$. For which integer value of k greater than 2 is the mean of all values in the sequence form $$A_1$$ through $$A_k$$ equal to the median of those values?

a) 6
b) 7
c) 8
d) 9
e) 10

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Intern
Joined: 17 Jan 2019
Posts: 6
Re: In a certain sequence, the term [m]A_n[/m] is given  [#permalink]

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28 Jan 2019, 21:06
A1=16-3
A2=16-4
A3=16-1
A4=16+/-0
A5=16+1
A6=16+4
A7=16+3

The Median and the Mean of A1-A7 are both 16. k=7→(B)

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Senior Manager
Joined: 12 Sep 2017
Posts: 295
Re: In a certain sequence, the term [m]A_n[/m] is given  [#permalink]

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29 Jan 2019, 18:19
Afc0892 wrote:
In a certain sequence, the term $$A_n$$ is given by the formula $$A_n = 16 - \frac{(4-n)^3}{|n-4|}$$ for all positive integers n≠4, While $$A_4 = 16$$. For which integer value of k greater than 2 is the mean of all values in the sequence form $$A_1$$ through $$A_k$$ equal to the median of those values?

a) 6
b) 7
c) 8
d) 9
e) 10

Hello Afc0892 !

Could you please provide the explanation?

Director
Joined: 27 May 2012
Posts: 816
Re: In a certain sequence, the term [m]A_n[/m] is given  [#permalink]

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18 Mar 2019, 05:22
jinghao wrote:
A1=16-3
A2=16-4
A3=16-1
A4=16+/-0
A5=16+1
A6=16+4
A7=16+3

The Median and the Mean of A1-A7 are both 16. k=7→(B)

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Hi jinghao
A1= 7
A2=12
A3=15
A4=16
A5=17
A6=20
A7=25

Mean = $$\frac{7+12+15.....25}{7}$$=16
Median =16
hence B
jfranciscocuencag, let me know if anything is still unclear.
Re: In a certain sequence, the term [m]A_n[/m] is given   [#permalink] 18 Mar 2019, 05:22
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