For which (n) will (S_n-S_{n-1}=37)?
Answer and explanation
Correct answer: 37
The sum of the first n natural numbers is
\(S_n=1+2+\cdots+n\), whereas
\(S_{n-1}=1+2+\cdots+(n-1)\). Therefore,
\(S_n-S_{n-1}=n\). Since the given difference is 37,
\(n=37\). For n = 36 or 38, the difference would be 36 or 38 respectively. Exam tip: the difference between two consecutive partial sums is the newly added term.
Frequently asked questions
What is the correct answer to this question?
37
Why is this the correct answer?
The sum of the first n natural numbers is
\(S_n=1+2+\cdots+n\), whereas
\(S_{n-1}=1+2+\cdots+(n-1)\). Therefore,
\(S_n-S_{n-1}=n\). Since the given difference is 37,
\(n=37\). For n = 36 or 38, the difference would be 36 or 38 respectively. Exam tip: the difference between two consecutive partial sums is the newly added term.
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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