What is the average of even numbers from 103 to 195? Here we will show you how to calculate the average of even numbers from 103 to 195.
To find the average of the even numbers from 103 to 195, we first calculate how many even numbers there are from 103 to 195. Then, we calculate the sum of even numbers from 103 to 195. And finally, we divide the sum by the number of even numbers to get the average.
The range is from 103 to 195, and the even numbers within that range are from 104 to 194. Therefore, the first even number in the sequence is 104, and the last even number in the sequence is 194.
Step 1) Calculate the total number of even numbers from 103 to 195
Here we calculate the total number of even numbers from 103 to 195 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 = (194 - 104 + 2) ÷ 2
tot = 92 ÷ 2
tot = 46
Total even numbers from 103 to 195 = 46
Step 2) Calculate the sum of even numbers from 103 to 195
To calculate the sum of even numbers from 103 to 195, 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 = (46 ÷ 2) × (2 × 104 + (2 × (46 - 1))
sum = 23 × (208 + 90)
sum = 23 × 298
sum = 6854
Sum of even numbers from 103 to 195 = 6854
Step 3) Calculate the average of even numbers from 103 to 195
Almost done! Now we can calculate the average of even numbers from 103 to 195 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 = 6854 ÷ 46
Average = 149
Average of even numbers from 103 to 195 = 149
Average of Even Numbers Calculator
Here you can calculate the average of even numbers of a different sequence.