What is the average of odd numbers from 2 to 169? Here we will show you how to calculate the average of odd numbers from 2 to 169.
To find the average of the odd numbers from 2 to 169, we first calculate how many odd numbers there are from 2 to 169. Then, we calculate the sum of odd numbers from 2 to 169. And finally, we divide the sum by the number of odd numbers to get the average.
The range is from 2 to 169, and the odd numbers within that range are from 3 to 169. Therefore, the first odd number in the sequence is 3, and the last odd number in the sequence is 169.
Step 1) Calculate the total number of odd numbers from 2 to 169
Here we calculate the total number of odd numbers from 2 to 169 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 = (169 - 3 + 2) ÷ 2
tot = 168 ÷ 2
tot = 84
Total odd numbers from 2 to 169 = 84
Step 2) Calculate the sum of odd numbers from 2 to 169
To calculate the sum of odd numbers from 2 to 169, 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 = (84 ÷ 2) × (2 × 3 + (2 × (84 - 1))
sum = 42 × (6 + 166)
sum = 42 × 172
sum = 7224
Sum of odd numbers from 2 to 169 = 7224
Step 3) Calculate the average of odd numbers from 2 to 169
Almost done! Now we can calculate the average of odd numbers from 2 to 169 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 = 7224 ÷ 84
Average = 86
Average of odd numbers from 2 to 169 = 86
Average of Odd Numbers Calculator
Here you can calculate the average of odd numbers of a different sequence.