Which number should be added to (S_{44}) to get (S_{50})?
Answer and explanation
Correct answer: \(285\)
Here, \(S_n\) denotes the sum of the first \(n\) natural numbers. Therefore, \(S_{50}-S_{44}\) contains only the terms from 45 to 50: \(45+46+47+48+49+50=285\). Hence, adding \(285\) to \(S_{44}\) gives \(S_{50}\). An option such as \(279\) is incorrect because it is not the complete sum of these six consecutive terms. Exam tip: To find \(S_b-S_a\), add the terms from \(a+1\) to \(b\).
Frequently asked questions
What is the correct answer to this question?
\(285\)
Why is this the correct answer?
Here, \(S_n\) denotes the sum of the first \(n\) natural numbers. Therefore, \(S_{50}-S_{44}\) contains only the terms from 45 to 50: \(45+46+47+48+49+50=285\). Hence, adding \(285\) to \(S_{44}\) gives \(S_{50}\). An option such as \(279\) is incorrect because it is not the complete sum of these six consecutive terms. Exam tip: To find \(S_b-S_a\), add the terms from \(a+1\) to \(b\).
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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