If (a_n=n^2+cn) and (a_4=32), what will be the value of (a_9)?
Answer and explanation
Correct answer: 117
Given \(a_n=n^2+cn\), substitute \(n=4\): \(a_4=4^2+4c=32\). Thus, \(16+4c=32\), so \(c=4\). Now substitute \(n=9\): \(a_9=9^2+4\times9=81+36=117\). Therefore, the correct answer is 117. Option 114 is close, but it is 3 less than the correct value of \(a_9\). 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?
117
Why is this the correct answer?
Given \(a_n=n^2+cn\), substitute \(n=4\): \(a_4=4^2+4c=32\). Thus, \(16+4c=32\), so \(c=4\). Now substitute \(n=9\): \(a_9=9^2+4\times9=81+36=117\). Therefore, the correct answer is 117. Option 114 is close, but it is 3 less than the correct value of \(a_9\). 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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