If (S_{n+2}-S_n=155), what is the value of (n)?
Answer and explanation
Correct answer: 76
Let \(S_n\) be the sum of the first \(n\) natural numbers. In \(S_{n+2}-S_n\), the common initial terms cancel, leaving \((n+1)+(n+2)=2n+3\). Thus, \(2n+3=155\), so \(2n=152\) and \(n=76\). If \(n=77\), the difference would be \(157\), not \(155\). Exam tip: In differences of sums, cancel the common terms and add only the remaining terms.
Frequently asked questions
What is the correct answer to this question?
76
Why is this the correct answer?
Let \(S_n\) be the sum of the first \(n\) natural numbers. In \(S_{n+2}-S_n\), the common initial terms cancel, leaving \((n+1)+(n+2)=2n+3\). Thus, \(2n+3=155\), so \(2n=152\) and \(n=76\). If \(n=77\), the difference would be \(157\), not \(155\). Exam tip: In differences of sums, cancel the common terms and add only the remaining 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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