If (S_n-S_{n-2}=101), what is the value of (S_n)?
Answer and explanation
Correct answer: 1326
Here, \(S_n\) is the sum of the first \(n\) natural numbers. In \(S_n-S_{n-2}\), the first \(n-2\) terms cancel, leaving \((n-1)+n=2n-1\). Thus, \(2n-1=101\) gives \(n=51\). Therefore, \(S_{51}=\frac{51\times52}{2}=1326\). Option 1275 is \(S_{50}\), so it is close but not correct. Exam tip: In differences of partial sums, cancel the common initial terms and write the remaining terms.
Frequently asked questions
What is the correct answer to this question?
1326
Why is this the correct answer?
Here, \(S_n\) is the sum of the first \(n\) natural numbers. In \(S_n-S_{n-2}\), the first \(n-2\) terms cancel, leaving \((n-1)+n=2n-1\). Thus, \(2n-1=101\) gives \(n=51\). Therefore, \(S_{51}=\frac{51\times52}{2}=1326\). Option 1275 is \(S_{50}\), so it is close but not correct. Exam tip: In differences of partial sums, cancel the common initial terms and write 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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