What is the average of even numbers from 109 to 148? Here we will show you how to calculate the average of even numbers from 109 to 148.
To find the average of the even numbers from 109 to 148, we first calculate how many even numbers there are from 109 to 148. Then, we calculate the sum of even numbers from 109 to 148. And finally, we divide the sum by the number of even numbers to get the average.
The range is from 109 to 148, and the even numbers within that range are from 110 to 148. Therefore, the first even number in the sequence is 110, and the last even number in the sequence is 148.
Step 1) Calculate the total number of even numbers from 109 to 148
Here we calculate the total number of even numbers from 109 to 148 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 = (148 - 110 + 2) ÷ 2
tot = 40 ÷ 2
tot = 20
Total even numbers from 109 to 148 = 20
Step 2) Calculate the sum of even numbers from 109 to 148
To calculate the sum of even numbers from 109 to 148, 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 = (20 ÷ 2) × (2 × 110 + (2 × (20 - 1))
sum = 10 × (220 + 38)
sum = 10 × 258
sum = 2580
Sum of even numbers from 109 to 148 = 2580
Step 3) Calculate the average of even numbers from 109 to 148
Almost done! Now we can calculate the average of even numbers from 109 to 148 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 = 2580 ÷ 20
Average = 129
Average of even numbers from 109 to 148 = 129
Average of Even Numbers Calculator
Here you can calculate the average of even numbers of a different sequence.