If (S_m=210) and (S_n=325), what is the value of (n-m)?
Answer and explanation
Correct answer: 5
The sum of the first k natural numbers is \(S_k=\frac{k(k+1)}{2}\). From \(\frac{m(m+1)}{2}=210\), we get \(m=20\); and from \(\frac{n(n+1)}{2}=325\), we get \(n=25\). Therefore, \(n-m=25-20=5\). Option 4 would result from incorrectly finding the difference between the indices. Exam tip: match a given sum with nearby triangular numbers to identify the index quickly.
Frequently asked questions
What is the correct answer to this question?
5
Why is this the correct answer?
The sum of the first k natural numbers is \(S_k=\frac{k(k+1)}{2}\). From \(\frac{m(m+1)}{2}=210\), we get \(m=20\); and from \(\frac{n(n+1)}{2}=325\), we get \(n=25\). Therefore, \(n-m=25-20=5\). Option 4 would result from incorrectly finding the difference between the indices. Exam tip: match a given sum with nearby triangular numbers to identify the index quickly.
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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