What is the average of even numbers from 1 to 157? Here we will show you how to calculate the average of even numbers from 1 to 157.
To find the average of the even numbers from 1 to 157, we first calculate how many even numbers there are from 1 to 157. Then, we calculate the sum of even numbers from 1 to 157. And finally, we divide the sum by the number of even numbers to get the average.
The range is from 1 to 157, and the even numbers within that range are from 2 to 156. Therefore, the first even number in the sequence is 2, and the last even number in the sequence is 156.
Step 1) Calculate the total number of even numbers from 1 to 157
Here we calculate the total number of even numbers from 1 to 157 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 = (156 - 2 + 2) ÷ 2
tot = 156 ÷ 2
tot = 78
Total even numbers from 1 to 157 = 78
Step 2) Calculate the sum of even numbers from 1 to 157
To calculate the sum of even numbers from 1 to 157, 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 = (78 ÷ 2) × (2 × 2 + (2 × (78 - 1))
sum = 39 × (4 + 154)
sum = 39 × 158
sum = 6162
Sum of even numbers from 1 to 157 = 6162
Step 3) Calculate the average of even numbers from 1 to 157
Almost done! Now we can calculate the average of even numbers from 1 to 157 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 = 6162 ÷ 78
Average = 79
Average of even numbers from 1 to 157 = 79
Average of Even Numbers Calculator
Here you can calculate the average of even numbers of a different sequence.