If (S_n=13041), what is the value of (n)?
Answer and explanation
Correct answer: 161
The sum of the first n natural numbers is \(S_n=\frac{n(n+1)}{2}\). Thus, \(\frac{n(n+1)}{2}=13041\), so \(n(n+1)=26082\). Since \(161\times162=26082\), \(n=161\). For example, \(n=160\) gives \(\frac{160\times161}{2}=12880\), not 13041. Exam tip: when a sum is given, multiply it by 2 and look for a product of consecutive integers.
Frequently asked questions
What is the correct answer to this question?
161
Why is this the correct answer?
The sum of the first n natural numbers is \(S_n=\frac{n(n+1)}{2}\). Thus, \(\frac{n(n+1)}{2}=13041\), so \(n(n+1)=26082\). Since \(161\times162=26082\), \(n=161\). For example, \(n=160\) gives \(\frac{160\times161}{2}=12880\), not 13041. Exam tip: when a sum is given, multiply it by 2 and look for a product of consecutive integers.
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.
