What is the average of first 15 odd numbers among the natural numbers?...
Here the first 15 odd natural number are
1 , 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23,25, 27, 29
Sum of first 15 odd numbers are 1 + 3 + 5 ....... + 29 = 225
Hence the average is = 225/15 = 15
What is the average of first 15 odd numbers among the natural numbers?...
Understanding Odd Numbers
Odd numbers are integers that are not divisible by 2. The first 15 odd numbers in the sequence of natural numbers are:
1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29.
Calculating the Sum of the First 15 Odd Numbers
To find the average, we first need to calculate the sum of these numbers.
- The sum can be calculated as follows:
- Sum = 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23 + 25 + 27 + 29
- Alternatively, we can use the formula for the sum of the first n odd numbers, which is n². Here, n = 15.
- So, Sum = 15² = 225.
Finding the Average
Once we have the sum, we can find the average by dividing the sum by the total number of terms (which is 15).
- Average = Sum / Total Numbers
- Average = 225 / 15 = 15.
Conclusion
Thus, the average of the first 15 odd numbers is:
- Option B: 15.
This means the correct answer to the question is indeed option 'B'.