Finding the Average of Multiples of Ten

To find the average of all the multiples of ten from 10 to 190 inclusive, we need to follow these steps:

Step 1: Find the number of terms in the series.
Step 2: Find the sum of all the terms.
Step 3: Divide the sum by the number of terms to get the average.

Step 1: Finding the Number of Terms

The series of multiples of ten from 10 to 190 inclusive can be written as:

10, 20, 30, ..., 190

We can find the number of terms using the formula:

number of terms = (last term - first term) / common difference + 1

In this case, the first term is 10, the last term is 190, and the common difference is 10. Plugging these values into the formula, we get:

number of terms = (190 - 10) / 10 + 1 = 19

Therefore, there are 19 terms in the series.

Step 2: Finding the Sum of All the Terms

We can find the sum of all the terms using the formula:

sum of terms = (first term + last term) / 2 * number of terms

Plugging in the values we found in step 1, we get:

sum of terms = (10 + 190) / 2 * 19 = 1000

Therefore, the sum of all the terms is 1000.

Step 3: Finding the Average

To find the average, we divide the sum by the number of terms:

average = sum of terms / number of terms = 1000 / 19 = 52.63

However, the question asks us to round to the nearest whole number. When we round 52.63 to the nearest whole number, we get 53. Therefore, the average of all the multiples of ten from 10 to 190 inclusive is 100.