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

A90
B95
C100
D105
E110

letter C: 100

Step-by-step explanation:

This problem can be configured as an arithmetic progression:

The first value is 10, the ratio is also 10 (the multiples of ten are 20, 30, 40, ...) and the number of terms is 19 (10, 20, 30, ... , 180, 190 -> total of 19 numbers).

So, we can use the following formula to calculate the sum of all these numbers:

Sn = n(a1 + an) /2

where Sn is the sum, n is the number of terms, a1 is the first term and an is the last one.

The result we want is the average of the sum, so we need to divide Sn by n:

Average = Sn/n = n(a1 + an) /2n = (a1 + an) /2 = (10+190)/2 = 200/2 = 100

The correct option is letter C.