If (a_n=n^2+cn) and (a_3=18), what is the value of (c)?
Answer and explanation
Correct answer: 3
Given \(a_n=n^2+cn\), substitute \(n=3\): \(a_3=3^2+3c=9+3c\). Since \(a_3=18\), \(9+3c=18\), so \(3c=9\) and \(c=3\). Therefore, option 3 is correct. If \(c=2\), then \(a_3=9+6=15\), not 18. Exam tip: substitute the specified value of \(n\) directly into the general term.
Frequently asked questions
What is the correct answer to this question?
3
Why is this the correct answer?
Given \(a_n=n^2+cn\), substitute \(n=3\): \(a_3=3^2+3c=9+3c\). Since \(a_3=18\), \(9+3c=18\), so \(3c=9\) and \(c=3\). Therefore, option 3 is correct. If \(c=2\), then \(a_3=9+6=15\), not 18. Exam tip: substitute the specified value of \(n\) directly into the general term.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: Explicit or general rule.
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