If (S_p=378) and (S_q=528), what is the value of (q-p)?
Answer and explanation
Correct answer: 5
The sum of the first n natural numbers is \(S_n=\frac{n(n+1)}{2}\). From \(\frac{p(p+1)}{2}=378\), we get \(p=27\), and from \(\frac{q(q+1)}{2}=528\), we get \(q=32\). Therefore, \(q-p=32-27=5\). Option 4 may seem close, but the corresponding indices for 378 and 528 are 27 and 32 respectively. Exam tip: write the sum as \(\frac{n(n+1)}{2}\) and identify the consecutive factors.
Frequently asked questions
What is the correct answer to this question?
5
Why is this the correct answer?
The sum of the first n natural numbers is \(S_n=\frac{n(n+1)}{2}\). From \(\frac{p(p+1)}{2}=378\), we get \(p=27\), and from \(\frac{q(q+1)}{2}=528\), we get \(q=32\). Therefore, \(q-p=32-27=5\). Option 4 may seem close, but the corresponding indices for 378 and 528 are 27 and 32 respectively. Exam tip: write the sum as \(\frac{n(n+1)}{2}\) and identify the consecutive factors.
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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