What is the average of even numbers from 1 to 1270? Here we will show you how to calculate the average of even numbers from 1 to 1270.
To find the average of the even numbers from 1 to 1270, we first calculate how many even numbers there are from 1 to 1270. Then, we calculate the sum of even numbers from 1 to 1270. And finally, we divide the sum by the number of even numbers to get the average.
The range is from 1 to 1270, and the even numbers within that range are from 2 to 1270. Therefore, the first even number in the sequence is 2, and the last even number in the sequence is 1270.
Step 1) Calculate the total number of even numbers from 1 to 1270
Here we calculate the total number of even numbers from 1 to 1270 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 = (1270 - 2 + 2) ÷ 2
tot = 1270 ÷ 2
tot = 635
Total even numbers from 1 to 1270 = 635
Step 2) Calculate the sum of even numbers from 1 to 1270
To calculate the sum of even numbers from 1 to 1270, 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 = (635 ÷ 2) × (2 × 2 + (2 × (635 - 1))
sum = 317.5 × (4 + 1268)
sum = 317.5 × 1272
sum = 403860
Sum of even numbers from 1 to 1270 = 403860
Step 3) Calculate the average of even numbers from 1 to 1270
Almost done! Now we can calculate the average of even numbers from 1 to 1270 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 = 403860 ÷ 635
Average = 636
Average of even numbers from 1 to 1270 = 636
Average of Even Numbers Calculator
Here you can calculate the average of even numbers of a different sequence.