Find the value of (S_{140}-S_{130}+S_{10}).
Answer and explanation
Correct answer: 1410
Here, \(S_n\) denotes the sum of the first \(n\) natural numbers, so \(S_n=\frac{n(n+1)}{2}\). Thus, \(S_{140}=9870\), \(S_{130}=8515\), and \(S_{10}=55\). Therefore, \(S_{140}-S_{130}+S_{10}=9870-8515+55=1410\). Note that \(S_{140}-S_{130}\) is the sum of the numbers from 131 to 140; adding \(S_{10}\) gives 1410. Exam tip: You can also verify \(S_a-S_b\) by summing the terms from \(b+1\) to \(a\).
Frequently asked questions
What is the correct answer to this question?
1410
Why is this the correct answer?
Here, \(S_n\) denotes the sum of the first \(n\) natural numbers, so \(S_n=\frac{n(n+1)}{2}\). Thus, \(S_{140}=9870\), \(S_{130}=8515\), and \(S_{10}=55\). Therefore, \(S_{140}-S_{130}+S_{10}=9870-8515+55=1410\). Note that \(S_{140}-S_{130}\) is the sum of the numbers from 131 to 140; adding \(S_{10}\) gives 1410. Exam tip: You can also verify \(S_a-S_b\) by summing the terms from \(b+1\) to \(a\).
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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