If (S_{n+1}-S_{n-2}=150), what will be the value of (n)?
Answer and explanation
Correct answer: 50
Let \(S_n\) be the sum of the first \(n\) natural numbers. In \(S_{n+1}-S_{n-2}\), the common terms from 1 to \(n-2\) cancel, leaving \((n-1)+n+(n+1)\). Hence, \(S_{n+1}-S_{n-2}=3n=150\), so \(n=50\). If \(n=49\), the difference would be 147, not 150. Exam tip: In differences of sums, cancel the common initial terms and write the remaining consecutive terms.
Frequently asked questions
What is the correct answer to this question?
50
Why is this the correct answer?
Let \(S_n\) be the sum of the first \(n\) natural numbers. In \(S_{n+1}-S_{n-2}\), the common terms from 1 to \(n-2\) cancel, leaving \((n-1)+n+(n+1)\). Hence, \(S_{n+1}-S_{n-2}=3n=150\), so \(n=50\). If \(n=49\), the difference would be 147, not 150. Exam tip: In differences of sums, cancel the common initial terms and write the remaining 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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