What is the average (arithmetic mean) of all multiples of 10 from 10 to 200 inclusive?

What is the average (arithmetic mean) of all multiples of 10 from 10 to 200 inclusive?

Quiz

Answer/Solution

105

Steps/Work

This question can be solved with the Average Formula and 'bunching.'
We're asked for the average of all of the multiples of 10 from 10 to 200, inclusive.
To start, we can figure out the total number of terms rather easily:
1(10) = 10
2(10) = 20
...
20(10) = 200
So we know that there are 40 total numbers.
We can now figure out the SUM of those numbers with 'bunching':
10 + 200 = 210
20 + 190 = 210
30 + 180 = 210
Etc.
Since there are 20 total terms, this pattern will create 10 'pairs' of 210.
Thus, since the average = (Sum of terms)/(Number of terms), we have...
(10)(210)/(20) =105
Answer : B

General Calculator / Auto Solver

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

Calculated Answer

105

Step by Step Solution

In order to solve problem, you must evaluate (((n0 + n2) * ((n2 - n0) / n0 + 1)) / 2) / ((n2 - n0) / n0 + 1).

n0 =10
n1 =10
n2 =200