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If the sum of the first n natural numbers is 2550, what is the value of n? (2021

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Question: If the sum of the first n natural numbers is 2550, what is the value of n? (2021)

Options:

  1. 50
  2. 45
  3. 60
  4. 55

Correct Answer: 50

Exam Year: 2021

Solution: 

The sum of the first n natural numbers is given by the formula n(n + 1)/2. Setting this equal to 2550, we have n(n + 1) = 5100. Solving the quadratic equation n^2 + n - 5100 = 0 gives n = 50.

If the sum of the first n natural numbers is 2550, what is the value of n? (2021

Practice Questions

Q1
If the sum of the first n natural numbers is 2550, what is the value of n? (2021)
  1. 50
  2. 45
  3. 60
  4. 55

Questions & Step-by-Step Solutions

If the sum of the first n natural numbers is 2550, what is the value of n? (2021)
  • 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 2550, so we write n(n + 1)/2 = 2550.
  • Step 3: To eliminate the fraction, multiply both sides of the equation by 2. This gives us n(n + 1) = 5100.
  • Step 4: Rearrange the equation to form a standard quadratic equation: n^2 + n - 5100 = 0.
  • Step 5: Use the quadratic formula or factor the equation to find the value of n. In this case, we can factor it to find n = 50.
  • Sum of Natural Numbers – Understanding the formula for the sum of the first n natural numbers, which is n(n + 1)/2.
  • Quadratic Equations – Solving quadratic equations using the standard form ax^2 + bx + c = 0.
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