What is the average of even numbers from 7 to 140? Here we will show you how to calculate the average of even numbers from 7 to 140.
To find the average of the even numbers from 7 to 140, we first calculate how many even numbers there are from 7 to 140. Then, we calculate the sum of even numbers from 7 to 140. And finally, we divide the sum by the number of even numbers to get the average.
The range is from 7 to 140, and the even numbers within that range are from 8 to 140. Therefore, the first even number in the sequence is 8, and the last even number in the sequence is 140.
Step 1) Calculate the total number of even numbers from 7 to 140
Here we calculate the total number of even numbers from 7 to 140 by entering the first and last even number in the sequence into our formula. Here is the formula and the math:
tot = (last - first + 2) ÷ 2
tot = (140 - 8 + 2) ÷ 2
tot = 134 ÷ 2
tot = 67
Total even numbers from 7 to 140 = 67
Step 2) Calculate the sum of even numbers from 7 to 140
To calculate the sum of even numbers from 7 to 140, you enter the total even numbers (tot) from Step 1 and the first even number in the sequence into our formula. Here is the formula and the math:
sum = (tot ÷ 2) × (2 × first + (2 × (tot - 1))
sum = (67 ÷ 2) × (2 × 8 + (2 × (67 - 1))
sum = 33.5 × (16 + 132)
sum = 33.5 × 148
sum = 4958
Sum of even numbers from 7 to 140 = 4958
Step 3) Calculate the average of even numbers from 7 to 140
Almost done! Now we can calculate the average of even numbers from 7 to 140 by dividing the sum of even numbers from Step 2 by the total even numbers from Step 1. Here is the formula, the math, and the answer:
Average = sum ÷ tot
Average = 4958 ÷ 67
Average = 74
Average of even numbers from 7 to 140 = 74
Average of Even Numbers Calculator
Here you can calculate the average of even numbers of a different sequence.