If (S_a=2485) and (S_b=3570), what will be the value of (b-a)?
Answer and explanation
Correct answer: \(14\)
The sum of the first \(n\) natural numbers is \(S_n=\frac{n(n+1)}{2}\). From \(\frac{a(a+1)}{2}=2485\), we get \(a=70\), since \(\frac{70\times71}{2}=2485\). Similarly, \(\frac{b(b+1)}{2}=3570\) gives \(b=84\), since \(\frac{84\times85}{2}=3570\). Therefore, \(b-a=84-70=14\). A close distractor such as \(12\) may result from incorrectly identifying the indices. Exam tip: first express each given sum using \(\frac{n(n+1)}{2}\), then determine \(n\).
Frequently asked questions
What is the correct answer to this question?
\(14\)
Why is this the correct answer?
The sum of the first \(n\) natural numbers is \(S_n=\frac{n(n+1)}{2}\). From \(\frac{a(a+1)}{2}=2485\), we get \(a=70\), since \(\frac{70\times71}{2}=2485\). Similarly, \(\frac{b(b+1)}{2}=3570\) gives \(b=84\), since \(\frac{84\times85}{2}=3570\). Therefore, \(b-a=84-70=14\). A close distractor such as \(12\) may result from incorrectly identifying the indices. Exam tip: first express each given sum using \(\frac{n(n+1)}{2}\), then determine \(n\).
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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