Question

Calculate the average of all multiples of 10 from 2 to 198

Answer 1

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Answer 2

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.