If (S_n=465), what will be the value of (S_{n+5})?
Answer and explanation
Correct answer: \(630\)
The sum of the first \(n\) natural numbers is \(S_n=\frac{n(n+1)}{2}\). Thus, \(\frac{n(n+1)}{2}=465\) gives \(n(n+1)=930\), so \(n=30\). Therefore, \(S_{n+5}=S_{35}=\frac{35\times36}{2}=630\). Options such as \(635\) result from not applying the sum formula correctly for all terms from 31 to 35. Exam tip: first find \(n\) from the given sum, then substitute the new index in the formula.
Frequently asked questions
What is the correct answer to this question?
\(630\)
Why is this the correct answer?
The sum of the first \(n\) natural numbers is \(S_n=\frac{n(n+1)}{2}\). Thus, \(\frac{n(n+1)}{2}=465\) gives \(n(n+1)=930\), so \(n=30\). Therefore, \(S_{n+5}=S_{35}=\frac{35\times36}{2}=630\). Options such as \(635\) result from not applying the sum formula correctly for all terms from 31 to 35. Exam tip: first find \(n\) from the given sum, then substitute the new index in the formula.
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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