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If the sum of the first n natural numbers is 55, what is n?
If the sum of the first n natural numbers is 55, what is n?
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Practice Questions
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Q1
If the sum of the first n natural numbers is 55, what is n?
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n(n + 1)/2 = 55, solving gives n = 10.
Questions & Step-by-step Solutions
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Q: If the sum of the first n natural numbers is 55, what is n?
Solution:
n(n + 1)/2 = 55, solving gives n = 10.
Steps: 6
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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 the formula equal to 55, since we know the sum is 55. This gives us the equation n(n + 1)/2 = 55.
Step 3: To eliminate the fraction, multiply both sides of the equation by 2. This gives us n(n + 1) = 110.
Step 4: Now, we need to solve the equation n(n + 1) = 110. This means we need to find two consecutive numbers that multiply to 110.
Step 5: Start testing natural numbers for n. If n = 10, then n + 1 = 11. Check if 10 * 11 = 110. It does, so n = 10 is correct.
Step 6: Conclude that the value of n is 10.
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