Find the sum of all natural numbers from 1 to 25.
Answer and explanation
Correct answer: 325
The governing concept is the formula for the sum of the first n natural numbers: S_n = n(n + 1)/2. The integers from 1 to 25 are precisely the first 25 natural numbers, so n = 25. Hence S_25 = 25 × 26 / 2 = 25 × 13 = 325. Thus option B is correct. The answer can also be verified by pairing terms: 1 + 25 = 26, 2 + 24 = 26, and so forth. There are 12 complete pairs and the middle number 13 remains, so the total is 12 × 26 + 13 = 325. The other options result from an incorrect multiplication, an incorrect number of terms, or an inaccurate pairing.
Frequently asked questions
What is the correct answer to this question?
325
Why is this the correct answer?
The governing concept is the formula for the sum of the first n natural numbers: S_n = n(n + 1)/2. The integers from 1 to 25 are precisely the first 25 natural numbers, so n = 25. Hence S_25 = 25 × 26 / 2 = 25 × 13 = 325. Thus option B is correct. The answer can also be verified by pairing terms: 1 + 25 = 26, 2 + 24 = 26, and so forth. There are 12 complete pairs and the middle number 13 remains, so the total is 12 × 26 + 13 = 325. The other options result from an incorrect multiplication, an incorrect number of terms, or an inaccurate pairing.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Sum of first n natural numbers.
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