What is the average (arithmetic mean) of all the multiples of ten from 10 to 190 inclusive?

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The multiples of 10 from 10 to 190 form an arithmetic series. The first term of the series is 10 and the common difference is 10.

As the nth term of an arithmetic series is given by a + (n - 1)*d, we get

190 = 10 + 10*(n - 1)

=> 180 = 10*(n - 1)

=> n = 19

The sum of all the multiples of 10 from 10 to 190 inclusive is 10+20+30...190 = (19/2)*(10 + 190) = 1900

As there are 19 terms that add up to 1900, the average is 1900/19 =100.

The average of all the multiples of ten from 10 to 190 inclusive is 100.

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