If (a_n=4n+q) and (a_{3n}-a_n=96), what is the value of (n)?
Answer and explanation
Correct answer: \(12\)
Given \(a_n=4n+q\), we get \(a_{3n}=4(3n)+q=12n+q\). Hence, \(a_{3n}-a_n=(12n+q)-(4n+q)=8n\). Since \(8n=96\), \(n=12\). The constant \(q\) cancels when the two terms are subtracted, so it does not affect the value of \(n\). Exam tip: Substitute \(3n\) for \(n\) carefully before finding the difference.
Frequently asked questions
What is the correct answer to this question?
\(12\)
Why is this the correct answer?
Given \(a_n=4n+q\), we get \(a_{3n}=4(3n)+q=12n+q\). Hence, \(a_{3n}-a_n=(12n+q)-(4n+q)=8n\). Since \(8n=96\), \(n=12\). The constant \(q\) cancels when the two terms are subtracted, so it does not affect the value of \(n\). Exam tip: Substitute \(3n\) for \(n\) carefully before finding the difference.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Arithmetic Progressions (AP). Topic: Finding the $n$th term of an AP.
