What is the average of odd numbers from 1 to 421? Here we will show you how to calculate the average of odd numbers from 1 to 421.
To find the average of the odd numbers from 1 to 421, we first calculate how many odd numbers there are from 1 to 421. Then, we calculate the sum of odd numbers from 1 to 421. And finally, we divide the sum by the number of odd numbers to get the average.
The range is from 1 to 421, and the odd numbers within that range are from 1 to 421. Therefore, the first odd number in the sequence is 1, and the last odd number in the sequence is 421.
Step 1) Calculate the total number of odd numbers from 1 to 421
Here we calculate the total number of odd numbers from 1 to 421 by entering the first and last odd number in the sequence into our formula. Here is the formula and the math:
tot = (last - first + 2) ÷ 2
tot = (421 - 1 + 2) ÷ 2
tot = 422 ÷ 2
tot = 211
Total odd numbers from 1 to 421 = 211
Step 2) Calculate the sum of odd numbers from 1 to 421
To calculate the sum of odd numbers from 1 to 421, you enter the total odd numbers (tot) from Step 1 and the first odd number in the sequence into our formula. Here is the formula and the math:
sum = (tot ÷ 2) × (2 × first + (2 × (tot - 1))
sum = (211 ÷ 2) × (2 × 1 + (2 × (211 - 1))
sum = 105.5 × (2 + 420)
sum = 105.5 × 422
sum = 44521
Sum of odd numbers from 1 to 421 = 44521
Step 3) Calculate the average of odd numbers from 1 to 421
Almost done! Now we can calculate the average of odd numbers from 1 to 421 by dividing the sum of odd numbers from Step 2 by the total odd numbers from Step 1. Here is the formula, the math, and the answer:
Average = sum ÷ tot
Average = 44521 ÷ 211
Average = 211
Average of odd numbers from 1 to 421 = 211
Average of Odd Numbers Calculator
Here you can calculate the average of odd numbers of a different sequence.