If (a_n=n^2+kn) and (a_3=30), what will be the value of (a_6)?
Answer and explanation
Correct answer: 78
Given \(a_n=n^2+kn\). Substituting \(n=3\), \(a_3=3^2+3k=30\), so \(9+3k=30\). Hence, \(k=7\). Now, for \(n=6\), \(a_6=6^2+6(7)=36+42=78\). Therefore, option C is correct. The value \(84\) would result from an incorrect calculation. Exam tip: first use the given term to find the unknown constant, then substitute the required value of \(n\).
Frequently asked questions
What is the correct answer to this question?
78
Why is this the correct answer?
Given \(a_n=n^2+kn\). Substituting \(n=3\), \(a_3=3^2+3k=30\), so \(9+3k=30\). Hence, \(k=7\). Now, for \(n=6\), \(a_6=6^2+6(7)=36+42=78\). Therefore, option C is correct. The value \(84\) would result from an incorrect calculation. Exam tip: first use the given term to find the unknown constant, then substitute the required value of \(n\).
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Sequences.
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