Answer :
To find the average of the first 126 odd natural numbers, we can use a formula for the average of a sequence of odd numbers.
The odd numbers sequence can be represented as:
1, 3, 5, 7, ...,
In general, the [tex]n[/tex]-th odd number is given by the formula:
[tex]a_n = 2n - 1[/tex]
So, the first 126 odd numbers are:
1, 3, 5, ...,
To find the sum of the first [tex]n[/tex] odd numbers, we use the formula:
[tex]\text{Sum} = n^2[/tex]
For [tex]n = 126[/tex], the sum of the first 126 odd numbers is:
[tex]126^2 = 15876[/tex]
Now, the average of these numbers is the sum divided by the number of terms, so:
[tex]\text{Average} = \frac{15876}{126}[/tex]
Calculating this gives:
[tex]\text{Average} = 126[/tex]
Therefore, the average of the first 126 odd natural numbers is 126.
The correct multiple-choice option is: B) 126.
