What is the average of even numbers from 1 to 490? Here we will show you how to calculate the average of even numbers from 1 to 490.
To find the average of the even numbers from 1 to 490, we first calculate how many even numbers there are from 1 to 490. Then, we calculate the sum of even numbers from 1 to 490. And finally, we divide the sum by the number of even numbers to get the average.
The range is from 1 to 490, and the even numbers within that range are from 2 to 490. Therefore, the first even number in the sequence is 2, and the last even number in the sequence is 490.
Step 1) Calculate the total number of even numbers from 1 to 490
Here we calculate the total number of even numbers from 1 to 490 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 = (490 - 2 + 2) ÷ 2
tot = 490 ÷ 2
tot = 245
Total even numbers from 1 to 490 = 245
Step 2) Calculate the sum of even numbers from 1 to 490
To calculate the sum of even numbers from 1 to 490, 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 = (245 ÷ 2) × (2 × 2 + (2 × (245 - 1))
sum = 122.5 × (4 + 488)
sum = 122.5 × 492
sum = 60270
Sum of even numbers from 1 to 490 = 60270
Step 3) Calculate the average of even numbers from 1 to 490
Almost done! Now we can calculate the average of even numbers from 1 to 490 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 = 60270 ÷ 245
Average = 246
Average of even numbers from 1 to 490 = 246
Average of Even Numbers Calculator
Here you can calculate the average of even numbers of a different sequence.