If (S_n-S_{50}=1575), what is the value of (n)?
Answer and explanation
Correct answer: 75
The sum of the first n natural numbers is \(S_n=\frac{n(n+1)}{2}\). Here, \(S_n-S_{50}=1575\) and \(S_{50}=\frac{50\times51}{2}=1275\). Therefore, \(S_n=1575+1275=2850\). Now \(\frac{n(n+1)}{2}=2850\), so \(n(n+1)=5700=75\times76\). Hence, \(n=75\). The nearby option 80 does not give a difference of 1575 from \(S_{50}\). Exam tip: In such questions, first add the known \(S_k\) to find \(S_n\).
Frequently asked questions
What is the correct answer to this question?
75
Why is this the correct answer?
The sum of the first n natural numbers is \(S_n=\frac{n(n+1)}{2}\). Here, \(S_n-S_{50}=1575\) and \(S_{50}=\frac{50\times51}{2}=1275\). Therefore, \(S_n=1575+1275=2850\). Now \(\frac{n(n+1)}{2}=2850\), so \(n(n+1)=5700=75\times76\). Hence, \(n=75\). The nearby option 80 does not give a difference of 1575 from \(S_{50}\). Exam tip: In such questions, first add the known \(S_k\) to find \(S_n\).
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.
