Question

answer this maths problem.fast ​

Answer 1

Answer:

sum of n odd numbers = n/2(2a+(n-1)d)

mean= [n/2(2a+(n-1)d)]/n

then [n/2(2a+(n-1)d)]/n=n²/81

Now a=1. d=2 put in equation

and enjoy the answer

Answer 2

Answer :

n = 81

Step-by-step explanation :

The n odd natural numbers are

 1 , 3 , 5 , 7 , 9 , ... , n

The series are in AP.

First term, a = 1

common difference, d = 3 - 1 = 5 - 3 = 2

• we know that,

Sum of n terms in an AP is given by,

   $\boxed{\bf S_n=\frac{n}{2}[2a+(n-1)d]}$

 The sum of first n odd natural numbers,

      $=\frac{n}{2} [2(1)+(n-1)(2)]\\\\ =\frac{n}{2} [2+2n-2] \\\\ =\frac{n}{2} [2n] \\\\ =n^2$

• we also know,

   $\boxed{\bf Mean=\frac{Sum \ of \ observations}{number \ of \ observations}}$

Mean of first n odd natural numbers

    $=\frac{n^2}{n} \\\\ =n$

• Given, mean of first n odd natural numbers is n²/81

               $\bf n=\frac{n^2}{81} \\\\ n^2=81n \\\\ n=81$

∴ The value of n is 81