If (S_{3k}=1176), what will be the value of (k)?
Answer and explanation
Correct answer: \(16\)
The sum of the first \(n\) natural numbers is \(S_n=\frac{n(n+1)}{2}\). Here, \(S_{3k}=1176\), so \(\frac{3k(3k+1)}{2}=1176\). This gives \(3k=48\), since \(\frac{48\times49}{2}=1176\). Hence, \(k=\frac{48}{3}=16\). If \(k=15\), the index would be \(45\), whose sum is \(1035\), not \(1176\). Exam tip: first find the index \(n\) from the sum, then use \(n=3k\).
Frequently asked questions
What is the correct answer to this question?
\(16\)
Why is this the correct answer?
The sum of the first \(n\) natural numbers is \(S_n=\frac{n(n+1)}{2}\). Here, \(S_{3k}=1176\), so \(\frac{3k(3k+1)}{2}=1176\). This gives \(3k=48\), since \(\frac{48\times49}{2}=1176\). Hence, \(k=\frac{48}{3}=16\). If \(k=15\), the index would be \(45\), whose sum is \(1035\), not \(1176\). Exam tip: first find the index \(n\) from the sum, then use \(n=3k\).
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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