If (S_{2p}=820), what is the value of (p)?
Answer and explanation
Correct answer: 20
The sum of the first \(n\) natural numbers is \(S_n=\frac{n(n+1)}{2}\). Here, \(S_{2p}=820\), so \(\frac{2p(2p+1)}{2}=820\). Since \(\frac{40\times41}{2}=820\), we get \(2p=40\), hence \(p=20\). If \(p=19\), the index would be \(38\), whose sum is not 820. Exam tip: When a sum is given, equate it to \(n(n+1)/2\) and find the index \(n\) first.
Frequently asked questions
What is the correct answer to this question?
20
Why is this the correct answer?
The sum of the first \(n\) natural numbers is \(S_n=\frac{n(n+1)}{2}\). Here, \(S_{2p}=820\), so \(\frac{2p(2p+1)}{2}=820\). Since \(\frac{40\times41}{2}=820\), we get \(2p=40\), hence \(p=20\). If \(p=19\), the index would be \(38\), whose sum is not 820. Exam tip: When a sum is given, equate it to \(n(n+1)/2\) and find the index \(n\) first.
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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