What is the average of odd numbers from 1 to 3011? Here we will show you how to calculate the average of odd numbers from 1 to 3011.
To find the average of the odd numbers from 1 to 3011, we first calculate how many odd numbers there are from 1 to 3011. Then, we calculate the sum of odd numbers from 1 to 3011. And finally, we divide the sum by the number of odd numbers to get the average.
The range is from 1 to 3011, and the odd numbers within that range are from 1 to 3011. Therefore, the first odd number in the sequence is 1, and the last odd number in the sequence is 3011.
Step 1) Calculate the total number of odd numbers from 1 to 3011
Here we calculate the total number of odd numbers from 1 to 3011 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 = (3011 - 1 + 2) ÷ 2
tot = 3012 ÷ 2
tot = 1506
Total odd numbers from 1 to 3011 = 1506
Step 2) Calculate the sum of odd numbers from 1 to 3011
To calculate the sum of odd numbers from 1 to 3011, 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 = (1506 ÷ 2) × (2 × 1 + (2 × (1506 - 1))
sum = 753 × (2 + 3010)
sum = 753 × 3012
sum = 2268036
Sum of odd numbers from 1 to 3011 = 2268036
Step 3) Calculate the average of odd numbers from 1 to 3011
Almost done! Now we can calculate the average of odd numbers from 1 to 3011 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 = 2268036 ÷ 1506
Average = 1506
Average of odd numbers from 1 to 3011 = 1506
Average of Odd Numbers Calculator
Here you can calculate the average of odd numbers of a different sequence.