Math Problem Statement

The average of first 60 natural numbers? Question 1Answer

a. 31.5

b. 30

c. 30.5

d. 31

Solution

The average of the first nn natural numbers can be calculated using the formula:

Average=Sum of first n natural numbersn\text{Average} = \frac{\text{Sum of first } n \text{ natural numbers}}{n}

The sum of the first nn natural numbers is given by:

Sum=n×(n+1)2\text{Sum} = \frac{n \times (n + 1)}{2}

For n=60n = 60:

Sum=60×612=1830\text{Sum} = \frac{60 \times 61}{2} = 1830

So, the average is:

Average=183060=30.5\text{Average} = \frac{1830}{60} = 30.5

Thus, the correct answer is:

c. 30.5

Would you like a detailed explanation or have any questions?

Related Questions:

  1. What is the average of the first 100 natural numbers?
  2. What is the sum of the first 50 natural numbers?
  3. How would you find the average of the first 60 even numbers?
  4. How does the average of natural numbers compare to that of consecutive integers starting from 10?
  5. What is the formula for the sum of the first nn odd natural numbers?

Tip: To find the average of the first nn natural numbers, simply use the formula n+12\frac{n+1}{2}.

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Math Problem Analysis

Mathematical Concepts

Arithmetic
Averages
Sum of Natural Numbers

Formulas

Average of first n natural numbers = Sum of first n natural numbers / n
Sum of first n natural numbers = n * (n + 1) / 2

Theorems

Sum Formula for Natural Numbers

Suitable Grade Level

Grades 6-8