If (a_n=n^2+mn+4) and (a_2+a_4=46), what is the value of (m)?
Answer and explanation
Correct answer: 3
Given \(a_n=n^2+mn+4\), we get \(a_2=2^2+2m+4=8+2m\) and \(a_4=4^2+4m+4=20+4m\). Hence, \(a_2+a_4=28+6m=46\), so \(6m=18\) and \(m=3\). If \(m=4\), the sum would be 52, so it is not correct. Exam tip: substitute the value of \(n\) carefully in every term before combining like terms.
Frequently asked questions
What is the correct answer to this question?
3
Why is this the correct answer?
Given \(a_n=n^2+mn+4\), we get \(a_2=2^2+2m+4=8+2m\) and \(a_4=4^2+4m+4=20+4m\). Hence, \(a_2+a_4=28+6m=46\), so \(6m=18\) and \(m=3\). If \(m=4\), the sum would be 52, so it is not correct. Exam tip: substitute the value of \(n\) carefully in every term before combining like terms.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Sequences and Progressions. Topic: nth term.
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