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In the nth row of Pascal's Triangle where the first row is n, the arithmetic mean of the elements is 51.2 . What is the value of n?

supermanaccz  Oct 29, 2017
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 #1
avatar+322 
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Nevermind, I got it.

 

You guys can still do it for fun though!

supermanaccz  Oct 29, 2017
 #2
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OK. Just for fun !!!

51.2 x 10 =512

Log(512) / Log(2) =9th row !!.

Guest Oct 29, 2017
edited by Guest  Oct 29, 2017
 #3
avatar+78729 
+1

The sum of any row  = 2^n....starting with n = 0

 

And the number of elements in any row  =  n + 1

 

And the arithmetic mean is given by

 

Sum of the elements / their number

 

So we have

 

2^n  / [ n + 1]  =  51.2

 

2^n  =   51.2 n  +  51.2

 

We can solve this graphically  here : https://www.desmos.com/calculator/xfcfgqc9rb

 

So...the solution is n =  9  =   9th row 

 

And the sum of the elements in the 9th row = 512

 

And the aritmetic mean  is   [512] / [ 9 + 1 ]  =  512 / 10   =   51.2

 

 

cool cool cool

CPhill  Oct 29, 2017
edited by CPhill  Oct 29, 2017

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