If S₍ₘ₊₁₎ − Sₘ = 76, what is the value of m?
Answer and explanation
Correct answer: 75
The partial sum S₍ₘ₊₁₎ contains all terms of Sₘ plus the new term m + 1. Therefore S₍ₘ₊₁₎ − Sₘ = m + 1. The given equation becomes m + 1 = 76, so subtracting 1 from both sides gives m = 75. Hence option B is correct. A common mistake is to state that the difference equals m rather than m + 1; that would lead to option C. Option A comes from subtracting 2 instead of 1, and option D comes from adding instead of subtracting. The key governing concept is that the difference between consecutive partial sums equals the newly added term, whose index here is m + 1.
Frequently asked questions
What is the correct answer to this question?
75
Why is this the correct answer?
The partial sum S₍ₘ₊₁₎ contains all terms of Sₘ plus the new term m + 1. Therefore S₍ₘ₊₁₎ − Sₘ = m + 1. The given equation becomes m + 1 = 76, so subtracting 1 from both sides gives m = 75. Hence option B is correct. A common mistake is to state that the difference equals m rather than m + 1; that would lead to option C. Option A comes from subtracting 2 instead of 1, and option D comes from adding instead of subtracting. The key governing concept is that the difference between consecutive partial sums equals the newly added term, whose index here is m + 1.
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.
