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

#2**0 **

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**+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

CPhill
Oct 29, 2017