What will be the value of S₂₄ + S₂₆?
Answer and explanation
Correct answer: 651
Here Sₖ means the sum of the first k natural numbers, so the governing formula is Sₖ = k(k + 1)/2. Calculate both terms separately: S₂₄ = 24 × 25/2 = 300, and S₂₆ = 26 × 27/2 = 351. Their sum is 300 + 351 = 651, so option B is correct. It is important not to interpret S₂₄ + S₂₆ as S₅₀ or as a single sum with index 24 + 26; the notation represents two separate triangular-number sums. Option A omits part of the required addition, while options C and D reflect arithmetic or index errors. Direct substitution into the formula is the safest method.
Frequently asked questions
What is the correct answer to this question?
651
Why is this the correct answer?
Here Sₖ means the sum of the first k natural numbers, so the governing formula is Sₖ = k(k + 1)/2. Calculate both terms separately: S₂₄ = 24 × 25/2 = 300, and S₂₆ = 26 × 27/2 = 351. Their sum is 300 + 351 = 651, so option B is correct. It is important not to interpret S₂₄ + S₂₆ as S₅₀ or as a single sum with index 24 + 26; the notation represents two separate triangular-number sums. Option A omits part of the required addition, while options C and D reflect arithmetic or index errors. Direct substitution into the formula is the safest method.
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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