The value of Sₙ − S₍ₙ₋₁₎ + S₍ₙ₋₂₎ − S₍ₙ₋₃₎ is 100. What is n?
Answer and explanation
Correct answer: 51
For sums of the first natural numbers, Sₖ − S₍ₖ₋₁₎ = k. Apply this identity to both pairs: Sₙ − S₍ₙ₋₁₎ = n and S₍ₙ₋₂₎ − S₍ₙ₋₃₎ = n − 2. Thus the complete expression equals n + (n − 2) = 2n − 2. The corrected value is 100, so 2n − 2 = 100, giving 2n = 102 and n = 51. Hence option C is correct. The original value 99 would produce n = 50.5, which is not a natural-number index and makes the original MCQ invalid; it has therefore been corrected to 100. The signs must be grouped as the two consecutive-sum differences shown.
Frequently asked questions
What is the correct answer to this question?
51
Why is this the correct answer?
For sums of the first natural numbers, Sₖ − S₍ₖ₋₁₎ = k. Apply this identity to both pairs: Sₙ − S₍ₙ₋₁₎ = n and S₍ₙ₋₂₎ − S₍ₙ₋₃₎ = n − 2. Thus the complete expression equals n + (n − 2) = 2n − 2. The corrected value is 100, so 2n − 2 = 100, giving 2n = 102 and n = 51. Hence option C is correct. The original value 99 would produce n = 50.5, which is not a natural-number index and makes the original MCQ invalid; it has therefore been corrected to 100. The signs must be grouped as the two consecutive-sum differences shown.
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.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
