If the mean of the first n natural numbers is 10, what is the value of n?
Practice Questions
Q1
If the mean of the first n natural numbers is 10, what is the value of n?
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Questions & Step-by-Step Solutions
If the mean of the first n natural numbers is 10, what is the value of n?
Step 1: Understand that the mean (average) of the first n natural numbers is calculated using the formula: Mean = (Sum of the first n natural numbers) / n.
Step 2: The sum of the first n natural numbers can be calculated using the formula: Sum = n(n + 1) / 2.
Step 3: Substitute the sum formula into the mean formula: Mean = (n(n + 1) / 2) / n.
Step 4: Simplify the mean formula: Mean = (n + 1) / 2.
Step 5: Set the mean equal to 10, as given in the question: (n + 1) / 2 = 10.
Step 6: Multiply both sides of the equation by 2 to eliminate the fraction: n + 1 = 20.
Step 7: Subtract 1 from both sides to solve for n: n = 20 - 1.
