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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?

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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
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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
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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

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

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