If the sum of the first n natural numbers is 5050, what is the value of n? (2021)
Practice Questions
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Q1
If the sum of the first n natural numbers is 5050, what is the value of n? (2021)
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The sum of the first n natural numbers is given by the formula n(n + 1)/2. Setting this equal to 5050, we have n(n + 1)/2 = 5050. Solving for n gives n = 100.
Questions & Step-by-step Solutions
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Q
Q: If the sum of the first n natural numbers is 5050, what is the value of n? (2021)
Solution: The sum of the first n natural numbers is given by the formula n(n + 1)/2. Setting this equal to 5050, we have n(n + 1)/2 = 5050. Solving for n gives n = 100.
Steps: 11
Step 1: Understand that the sum of the first n natural numbers can be calculated using the formula n(n + 1)/2.
Step 2: Set up the equation using the given sum: n(n + 1)/2 = 5050.
Step 3: To eliminate the fraction, multiply both sides of the equation by 2: n(n + 1) = 10100.
Step 4: Now, we need to solve the equation n(n + 1) = 10100. This means we need to find two consecutive numbers that multiply to 10100.
Step 5: Rewrite the equation as n^2 + n - 10100 = 0. This is a quadratic equation.
Step 6: Use the quadratic formula n = (-b ± √(b² - 4ac)) / 2a, where a = 1, b = 1, and c = -10100.
