What is the average of even numbers from 1 to 1378? Here we will show you how to calculate the average of even numbers from 1 to 1378.
To find the average of the even numbers from 1 to 1378, we first calculate how many even numbers there are from 1 to 1378. Then, we calculate the sum of even numbers from 1 to 1378. And finally, we divide the sum by the number of even numbers to get the average.
The range is from 1 to 1378, and the even numbers within that range are from 2 to 1378. Therefore, the first even number in the sequence is 2, and the last even number in the sequence is 1378.
Step 1) Calculate the total number of even numbers from 1 to 1378
Here we calculate the total number of even numbers from 1 to 1378 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 = (1378 - 2 + 2) ÷ 2
tot = 1378 ÷ 2
tot = 689
Total even numbers from 1 to 1378 = 689
Step 2) Calculate the sum of even numbers from 1 to 1378
To calculate the sum of even numbers from 1 to 1378, 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 = (689 ÷ 2) × (2 × 2 + (2 × (689 - 1))
sum = 344.5 × (4 + 1376)
sum = 344.5 × 1380
sum = 475410
Sum of even numbers from 1 to 1378 = 475410
Step 3) Calculate the average of even numbers from 1 to 1378
Almost done! Now we can calculate the average of even numbers from 1 to 1378 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 = 475410 ÷ 689
Average = 690
Average of even numbers from 1 to 1378 = 690
Average of Even Numbers Calculator
Here you can calculate the average of even numbers of a different sequence.