What is the average of even numbers from 2 to 37? Here we will show you how to calculate the average of even numbers from 2 to 37.
To find the average of the even numbers from 2 to 37, we first calculate how many even numbers there are from 2 to 37. Then, we calculate the sum of even numbers from 2 to 37. And finally, we divide the sum by the number of even numbers to get the average.
The range is from 2 to 37, and the even numbers within that range are from 2 to 36. Therefore, the first even number in the sequence is 2, and the last even number in the sequence is 36.
Step 1) Calculate the total number of even numbers from 2 to 37
Here we calculate the total number of even numbers from 2 to 37 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 = (36 - 2 + 2) ÷ 2
tot = 36 ÷ 2
tot = 18
Total even numbers from 2 to 37 = 18
Step 2) Calculate the sum of even numbers from 2 to 37
To calculate the sum of even numbers from 2 to 37, 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 = (18 ÷ 2) × (2 × 2 + (2 × (18 - 1))
sum = 9 × (4 + 34)
sum = 9 × 38
sum = 342
Sum of even numbers from 2 to 37 = 342
Step 3) Calculate the average of even numbers from 2 to 37
Almost done! Now we can calculate the average of even numbers from 2 to 37 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 = 342 ÷ 18
Average = 19
Average of even numbers from 2 to 37 = 19
Average of Even Numbers Calculator
Here you can calculate the average of even numbers of a different sequence.