If S_(n+2) − S_(n−2) = 286, what is the value of n?
Answer and explanation
Correct answer: 71
For the sum of the first n natural numbers, S_r = 1 + 2 + ... + r. Therefore, S_(n+2) − S_(n−2) contains only the four terms that are added after S_(n−2): (n−1), n, (n+1), and (n+2). Their sum is (n−1) + n + (n+1) + (n+2) = 4n + 2. Equating this with the given value gives 4n + 2 = 286, so 4n = 284 and n = 71. Thus option D is correct. The other choices result from an arithmetic error while combining the four consecutive terms or while subtracting 2 from 286.
Frequently asked questions
What is the correct answer to this question?
71
Why is this the correct answer?
For the sum of the first n natural numbers, S_r = 1 + 2 + ... + r. Therefore, S_(n+2) − S_(n−2) contains only the four terms that are added after S_(n−2): (n−1), n, (n+1), and (n+2). Their sum is (n−1) + n + (n+1) + (n+2) = 4n + 2. Equating this with the given value gives 4n + 2 = 286, so 4n = 284 and n = 71. Thus option D is correct. The other choices result from an arithmetic error while combining the four consecutive terms or while subtracting 2 from 286.
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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