The mean of the first eight odd natural numbers is:

Correct option is C

Given:

First eight odd natural numbers.

Formula Used :

Sum of the first n terms of an AP:

​$$S_n = \frac{n}{2}[2a + (n-1)d]$$​​

Solution:

The first eight odd natural numbers are: 1, 3, 5, 7, 9, 11, 13, and 15.

Here, n = 8, a = 1, and d = 2.

​$$S_8 = \frac{8}{2}[2(1) + (8-1)(2)]$$​​

​$$S_8 = 4[2 + 7(2)]$$​​

​$$S_8 = 4[2 + 14]$$​​

​$$S_8 = 4[16]$$​​

​$$S_8 = 64$$​​

Mean = $$\frac{S_8}{8} = \frac{64}{8} = 8$$​​

Therefore, the mean of the first eight odd natural numbers is 8.

Alternate Method:

For the first n odd natural numbers, the sum is $$n^2.$$​​

In this case, we have the first 8 odd natural numbers, so their sum is $$8^2 = 64.$$​​

The mean is then the sum divided by the number of terms:$$\frac{64}{8} = 8.$$​​