If (S_a=1540) and (S_b=2080), what will be the value of (b-a)?
Answer and explanation
Correct answer: 9
The sum of the first n natural numbers is
\(S_n=\frac{n(n+1)}{2}\). From
\(\frac{a(a+1)}{2}=1540\), we get
\(a=55\), and from
\(\frac{b(b+1)}{2}=2080\), we get
\(b=64\). Therefore,
\(b-a=64-55=9\). Although 8 may seem close, the indices corresponding to the two given sums differ by exactly 9. Exam tip: equate the given sum to
\(\frac{n(n+1)}{2}\) and solve for n.
Frequently asked questions
What is the correct answer to this question?
9
Why is this the correct answer?
The sum of the first n natural numbers is
\(S_n=\frac{n(n+1)}{2}\). From
\(\frac{a(a+1)}{2}=1540\), we get
\(a=55\), and from
\(\frac{b(b+1)}{2}=2080\), we get
\(b=64\). Therefore,
\(b-a=64-55=9\). Although 8 may seem close, the indices corresponding to the two given sums differ by exactly 9. Exam tip: equate the given sum to
\(\frac{n(n+1)}{2}\) and solve for 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.
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