If (S_n=5050), what is the value of (S_{n-10})?
Answer and explanation
Correct answer: 4095
The sum of the first n natural numbers is \(S_n=\frac{n(n+1)}{2}\). Since \(5050=\frac{100\times101}{2}\), we get \(n=100\). Therefore, \(S_{n-10}=S_{90}=\frac{90\times91}{2}=4095\). Option 4186 is not correct because it is the sum of the first 91 natural numbers. Exam tip: Recognise 5050 as \(S_{100}\), then reduce the subscript by 10.
Frequently asked questions
What is the correct answer to this question?
4095
Why is this the correct answer?
The sum of the first n natural numbers is \(S_n=\frac{n(n+1)}{2}\). Since \(5050=\frac{100\times101}{2}\), we get \(n=100\). Therefore, \(S_{n-10}=S_{90}=\frac{90\times91}{2}=4095\). Option 4186 is not correct because it is the sum of the first 91 natural numbers. Exam tip: Recognise 5050 as \(S_{100}\), then reduce the subscript by 10.
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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