Calculate the average of all multiples of 10 from 2 to 198
Answers
Given:
Multiples of 10 between 2 and 198
To find:
The average of all such multiples
Solution:
The average of all multiples of 10 between 2 and 198 is 100.
We can find the average by following the steps given below-
We know that the average can be obtained by adding all the multiples and dividing with the number of multiples.
The sequence of multiples will form an arithmetic progression with 10 as the common difference.
The sequence becomes 10, 20, 30, and so on till 190.
Here, the first term, a=10
The last term, l=190
The common difference, d=10
So, the number of terms, n=(last term-first term)/common difference +1
n=(190-10)/10+1
n=18+1=19
The sum of the given sequence of multiples of 10=n/2×(2a+(n-1)d)
On putting the values,
=19/2×(2×10+(19-1)×10)
=19/2×(20+180)
=19/2×200
=1,900
Now, the average of all multiples of 10 between 2 and 198=Sum of all the multiples/ Number of multiples
=1,900/19
=100
Therefore, the average of all multiples of 10 between 2 and 198 is 100.