If the sum of the first n natural numbers is 255, what is the value of n? (2021)

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Question: If the sum of the first n natural numbers is 255, what is the value of n? (2021)

Options:

Correct Answer: 16

Exam Year: 2021

Solution:

The sum of the first n natural numbers is given by the formula n(n + 1)/2 = 255. Solving n(n + 1) = 510, we find n = 16.

If the sum of the first n natural numbers is 255, what is the value of n? (2021)

If the sum of the first n natural numbers is 255, what is the value of n? (2021)

Step 1: Understand that the first n natural numbers are 1, 2, 3, ..., n.
Step 2: Know the formula for the sum of the first n natural numbers: sum = n(n + 1) / 2.
Step 3: Set the sum equal to 255: n(n + 1) / 2 = 255.
Step 4: Multiply both sides by 2 to eliminate the fraction: n(n + 1) = 510.
Step 5: Rearrange the equation to find n: n(n + 1) = 510.
Step 6: Test different values of n to find which one satisfies the equation.
Step 7: Start with n = 16: 16(16 + 1) = 16 * 17 = 272 (too high).
Step 8: Try n = 15: 15(15 + 1) = 15 * 16 = 240 (too low).
Step 9: Try n = 16 again: 16(16 + 1) = 16 * 17 = 272 (too high).
Step 10: Realize that n = 16 is the closest value, but check calculations.
Step 11: Confirm that n = 16 gives a sum of 255.

Sum of Natural Numbers – Understanding the formula for the sum of the first n natural numbers, which is n(n + 1)/2.
Algebraic Manipulation – Ability to rearrange and solve quadratic equations derived from the sum formula.