Sum of the First 25 Natural Numbers — Apply the Standard Formula Compute the value of 1 + 2 + 3 + … + 25.

Introduction / Context:Summation formulas save time in arithmetic progressions. The series of the first n natural numbers has a well-known closed form, allowing you to compute large sums instantly without manual addition.

Given Data / Assumptions:

• We sum integers from 1 through 25 inclusive.
• Series is an arithmetic progression with first term 1, last term 25, common difference 1.

Concept / Approach:Use the formula S_n = n(n + 1)/2. This formula arises from pairing terms equidistant from the ends (1 with 25, 2 with 24, etc.), each pair summing to 26, with 12 full pairs and one middle term 13—equivalently handled by the formula.

Step-by-Step Solution:Identify n = 25.Apply S_n = n(n + 1)/2 = 25 * 26 / 2.Compute 26 / 2 = 13 → S_25 = 25 * 13.Multiply: 25 * 13 = 325.

Verification / Alternative check:Quick mental check: The average of numbers 1 to 25 is (1 + 25)/2 = 13. With 25 terms, total = 13 * 25 = 325. Matches the formula result.

Why Other Options Are Wrong:432, 315, 335, and 300 are off due to arithmetic mistakes or misuse of the formula.

Common Pitfalls:Forgetting to divide by 2; summing a subset (e.g., up to 24) by mistake; miscomputing 25 * 13 under time pressure.

Final Answer:325