If (S_a=351) and (S_b=465), what is (b-a)?
Answer and explanation
Correct answer: 4
The sum of the first n natural numbers is \(S_n=\frac{n(n+1)}{2}\). From \(\frac{a(a+1)}{2}=351\), we get \(a=26\), since \(\frac{26\times27}{2}=351\). Similarly, \(\frac{b(b+1)}{2}=465\) gives \(b=30\), since \(\frac{30\times31}{2}=465\). Therefore, \(b-a=30-26=4\). Option 3 is incorrect because it is one less than the actual difference between the two indices. Exam tip: equate each given sum to \(\frac{n(n+1)}{2}\) to find its index.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
The sum of the first n natural numbers is \(S_n=\frac{n(n+1)}{2}\). From \(\frac{a(a+1)}{2}=351\), we get \(a=26\), since \(\frac{26\times27}{2}=351\). Similarly, \(\frac{b(b+1)}{2}=465\) gives \(b=30\), since \(\frac{30\times31}{2}=465\). Therefore, \(b-a=30-26=4\). Option 3 is incorrect because it is one less than the actual difference between the two indices. Exam tip: equate each given sum to \(\frac{n(n+1)}{2}\) to find its index.
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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