What is the average of even numbers from 1 to 1961? Here we will show you how to calculate the average of even numbers from 1 to 1961.
To find the average of the even numbers from 1 to 1961, we first calculate how many even numbers there are from 1 to 1961. Then, we calculate the sum of even numbers from 1 to 1961. And finally, we divide the sum by the number of even numbers to get the average.
The range is from 1 to 1961, and the even numbers within that range are from 2 to 1960. Therefore, the first even number in the sequence is 2, and the last even number in the sequence is 1960.
Step 1) Calculate the total number of even numbers from 1 to 1961
Here we calculate the total number of even numbers from 1 to 1961 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 = (1960 - 2 + 2) ÷ 2
tot = 1960 ÷ 2
tot = 980
Total even numbers from 1 to 1961 = 980
Step 2) Calculate the sum of even numbers from 1 to 1961
To calculate the sum of even numbers from 1 to 1961, 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 = (980 ÷ 2) × (2 × 2 + (2 × (980 - 1))
sum = 490 × (4 + 1958)
sum = 490 × 1962
sum = 961380
Sum of even numbers from 1 to 1961 = 961380
Step 3) Calculate the average of even numbers from 1 to 1961
Almost done! Now we can calculate the average of even numbers from 1 to 1961 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 = 961380 ÷ 980
Average = 981
Average of even numbers from 1 to 1961 = 981
Average of Even Numbers Calculator
Here you can calculate the average of even numbers of a different sequence.