Find the value of S₍₂₅₎ + S₍₂₇₎, where Sₙ denotes the sum of the first n natural numbers.
Answer and explanation
Correct answer: 703
The governing formula for the sum of the first n natural numbers is Sₙ = n(n + 1)/2. Therefore, S₂₅ = 25 × 26/2 = 25 × 13 = 325, and S₂₇ = 27 × 28/2 = 27 × 14 = 378. Adding the two required sums gives S₂₅ + S₂₇ = 325 + 378 = 703. Hence option A is correct. The nearby alternatives arise from an arithmetic error, such as using an incorrect consecutive number, miscomputing one of the two sums, or adding 325 and 378 incorrectly. The suffixes 25 and 27 must be evaluated separately; they do not represent one combined index.
Frequently asked questions
What is the correct answer to this question?
703
Why is this the correct answer?
The governing formula for the sum of the first n natural numbers is Sₙ = n(n + 1)/2. Therefore, S₂₅ = 25 × 26/2 = 25 × 13 = 325, and S₂₇ = 27 × 28/2 = 27 × 14 = 378. Adding the two required sums gives S₂₅ + S₂₇ = 325 + 378 = 703. Hence option A is correct. The nearby alternatives arise from an arithmetic error, such as using an incorrect consecutive number, miscomputing one of the two sums, or adding 325 and 378 incorrectly. The suffixes 25 and 27 must be evaluated separately; they do not represent one combined index.
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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