Calculating the Average of First 152 Odd Natural Numbers
The question asks for the average value of the first 152 odd natural numbers. Let's break down how to find this.
Understanding Odd Natural Numbers
Natural numbers are the positive whole numbers: 1, 2, 3, 4, and so on. Odd natural numbers are the natural numbers that are not divisible by 2: 1, 3, 5, 7, 9, ...
Formula for the Sum of Odd Numbers
There's a useful formula for the sum of the first '$n$' odd natural numbers: Sum = $n^2$
Formula for Average
The average of a set of numbers is calculated by dividing the sum of the numbers by the count of the numbers. Average = $\frac{\text{Sum of Numbers}}{\text{Count of Numbers}}$
Step-by-Step Calculation
In this problem:
- The count of numbers is $n = 152$.
- We need the sum of the first 152 odd natural numbers. Using the formula, the sum is: Sum = $152^2$
- Now, we calculate the average: Average = $\frac{\text{Sum}}{n}$ Average = $\frac{152^2}{152}$
- Simplifying the expression: Average = $152$
Conclusion
Therefore, the average of the first 152 odd natural numbers is exactly 152. This result aligns with a known property: the average of the first '$n$' odd natural numbers is always '$n$'.
Important Questions from Average
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- The sum of five numbers is 655. The average of the first two numbers is 80 and the third number is 101. Find the average of the remaining two numbers.
