If (a_n=6n+q) and (a_{5n}-a_n=216), what is the value of (n)?
Answer and explanation
Correct answer: \(9\)
Given \(a_n=6n+q\), we get \(a_{5n}=6(5n)+q=30n+q\). Hence, \(a_{5n}-a_n=(30n+q)-(6n+q)=24n\). Now \(24n=216\), so \(n=216/24=9\). Therefore, the correct option is \(9\). The term \(q\) cancels because it occurs in both terms. Exam tip: In such questions, first write \(a_{5n}\) explicitly and then subtract \(a_n\).
Frequently asked questions
What is the correct answer to this question?
\(9\)
Why is this the correct answer?
Given \(a_n=6n+q\), we get \(a_{5n}=6(5n)+q=30n+q\). Hence, \(a_{5n}-a_n=(30n+q)-(6n+q)=24n\). Now \(24n=216\), so \(n=216/24=9\). Therefore, the correct option is \(9\). The term \(q\) cancels because it occurs in both terms. Exam tip: In such questions, first write \(a_{5n}\) explicitly and then subtract \(a_n\).
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.
