Question

7. Find the mean of first n odd natural numbers​

Answer 1

Mean of first n odd numbers is n.

• Odd number starts from 1 .
• The series of odd numbers is 1 , 3 , 5 , 7, 9 , and so on.
• We have to find the mean of first n odd numbers.
• To obtain the mean of n numbers, we find the sum of n numbers and then divide the sum by n.
• Now to find the sum of n odd numbers , we see that the given odd numbers are in AP with first term(a) = 1 and common difference(d) = 2.
• Applying the formula of sum of n terms of AP,

Sum of n terms of AP = $\frac{n}{2}[2a + (n-1)d]$

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

• Substituting the value of a and d in the equation, we get

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

$S_n = \frac{n}{2}[2 + 2n - 2]$

$S_n = \frac{n}{2}[2n]$

$S_n = n^2$

• Now calculating mean of n odd number,

Dividing the sum by n, we get

Mean of n odd numbers = $\frac{S_n}{n}$ = $\frac{n^2}{n}$ = n.

Answer 2

Answer:

Step-by-step explanation:

n is the Answer