If (S_{n+2}-S_{n-2}=402), what will be the value of (n)?
Answer and explanation
Correct answer: 100
Here, \(S_r\) denotes the sum of the first \(r\) natural numbers. In \(S_{n+2}-S_{n-2}\), the terms from \(1\) to \(n-2\) cancel, leaving \((n-1)+n+(n+1)+(n+2)=4n+2\). Thus, \(4n+2=402\), so \(4n=400\) and \(n=100\). Hence, 100 is correct. For the closest distractor, \(n=99\) would give a difference of \(398\), not 402. Exam tip: when subtracting partial sums, write only the uncancelled consecutive terms.
Frequently asked questions
What is the correct answer to this question?
100
Why is this the correct answer?
Here, \(S_r\) denotes the sum of the first \(r\) natural numbers. In \(S_{n+2}-S_{n-2}\), the terms from \(1\) to \(n-2\) cancel, leaving \((n-1)+n+(n+1)+(n+2)=4n+2\). Thus, \(4n+2=402\), so \(4n=400\) and \(n=100\). Hence, 100 is correct. For the closest distractor, \(n=99\) would give a difference of \(398\), not 402. Exam tip: when subtracting partial sums, write only the uncancelled consecutive terms.
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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