If (S_n=2080), what will be the value of (S_{n+9})?
Answer and explanation
Correct answer: 2701
The sum of the first \(n\) natural numbers is \(S_n=\frac{n(n+1)}{2}\). From \(\frac{n(n+1)}{2}=2080\), we get \(n=64\). Hence, \(n+9=73\), so \(S_{n+9}=S_{73}=\frac{73\times74}{2}=2701\). A value such as 2651 may result from using an incorrect index or an addition error. Exam tip: first find \(n\) from the given sum, then substitute the new index.
Frequently asked questions
What is the correct answer to this question?
2701
Why is this the correct answer?
The sum of the first \(n\) natural numbers is \(S_n=\frac{n(n+1)}{2}\). From \(\frac{n(n+1)}{2}=2080\), we get \(n=64\). Hence, \(n+9=73\), so \(S_{n+9}=S_{73}=\frac{73\times74}{2}=2701\). A value such as 2651 may result from using an incorrect index or an addition error. Exam tip: first find \(n\) from the given sum, then substitute the new index.
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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