What is the average of the integers from 2 to 105? Here we will show you how to calculate the average of the integers from 2 to 105.
To calculate the average of any set of numbers, you divide the sum of the numbers by the total numbers in the set (Sum/Total).
Therefore, to calculate the average of the integers from 2 to 105, we need to divide the sum of the integers from 2 and 105 by the total number of integers from 2 to 105. Here are step-by-step instructions:
Step 1) Calculate Sum of Numbers
First, we calculate the sum of all the integers (whole numbers) from 2 to 105 by using a formula where a is the low number of 2 and b is the high number of 105:
Sum = ((b - a + 1) ÷ 2) × (a + b)
Sum = ((105 - 2 + 1) ÷ 2) × (2 + 105)
Sum = (104 ÷ 2) × (107)
Sum = 52 × 107
Sum of Numbers = 5564
Step 2) Calculate Total Number
Next, we calculate the total number of integers from 2 to 105. To calculate the total number of integers, we calculate the difference between 2 and 105 and then add 1. Here is the formula and the math. Once again, a is the low number of 2 and b is the high number of 105:
Total = b - a + 1
Total = 105 - 2 + 1
Total Number = 104
Step 3) Calculate the Average
Now we have both pieces needed to calculate the average of the integers from 2 to 105. We calculate the average of the integers by dividing the Sum of Numbers from Step 1 by the Total Number from Step 2. Here is the math and the answer:
Average = Sum of Numbers ÷ Total Number
Average = 5564 ÷ 104
Average = 53.5
Average of Integers in a Sequence Calculator
Use this calculator to calculate the average of integers in a sequence.