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The average of the first 10 natural numbers is:
5
6
5.5
6.5
5
For the first 'n' natural numbers, the average is simply the middle value between 1 and 'n', calculated as (n + 1) / 2.
We need to find the average of the first 10 natural numbers.
Average=nSumтАЛ=2n+1тАЛ
For the first 'n' natural numbers, the average is simply the middle value between 1 and 'n', calculated as (n + 1) / 2.
Many students mistake natural numbers starting from 0, but natural numbers (counting numbers) start from 1.
Identify the set of numbers
The first 10 natural numbers are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
Set={1,2,3,4,5,6,7,8,9,10}
Calculate the sum
Sum of first n natural numbers is given by the formula 2n(n+1)тАЛ. For n=10, sum is 210├Ч11тАЛ=55.
Sum=210(11)тАЛ=55
Calculate the average
The average is the sum divided by the total count n=10.
Average=1055тАЛ=5.5
C is correct because the average of the first 10 natural numbers is calculated as (1+10)/2 = 5.5.
This formula 2n+1тАЛ applies to any Arithmetic Progression (AP) where the average is simply the average of the first and last terms: 2first+lastтАЛ.
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