What is the average of even numbers from 7 to 145? Here we will show you how to calculate the average of even numbers from 7 to 145.
To find the average of the even numbers from 7 to 145, we first calculate how many even numbers there are from 7 to 145. Then, we calculate the sum of even numbers from 7 to 145. And finally, we divide the sum by the number of even numbers to get the average.
The range is from 7 to 145, and the even numbers within that range are from 8 to 144. Therefore, the first even number in the sequence is 8, and the last even number in the sequence is 144.
Step 1) Calculate the total number of even numbers from 7 to 145
Here we calculate the total number of even numbers from 7 to 145 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 = (144 - 8 + 2) ÷ 2
tot = 138 ÷ 2
tot = 69
Total even numbers from 7 to 145 = 69
Step 2) Calculate the sum of even numbers from 7 to 145
To calculate the sum of even numbers from 7 to 145, 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 = (69 ÷ 2) × (2 × 8 + (2 × (69 - 1))
sum = 34.5 × (16 + 136)
sum = 34.5 × 152
sum = 5244
Sum of even numbers from 7 to 145 = 5244
Step 3) Calculate the average of even numbers from 7 to 145
Almost done! Now we can calculate the average of even numbers from 7 to 145 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 = 5244 ÷ 69
Average = 76
Average of even numbers from 7 to 145 = 76
Average of Even Numbers Calculator
Here you can calculate the average of even numbers of a different sequence.