If (a_n=10n+q) and (a_{7n}-a_{3n}=520), what is the value of (n)?
Answer and explanation
Correct answer: 13
Given \(a_n=10n+q\), we get \(a_{7n}=70n+q\) and \(a_{3n}=30n+q\). Hence, \(a_{7n}-a_{3n}=(70n+q)-(30n+q)=40n\). Therefore, \(40n=520\), so \(n=13\). The constant \(q\) cancels because it occurs in both terms. Exam tip: for terms such as \(a_{7n}\) and \(a_{3n}\), directly substitute \(7n\) and \(3n\) respectively in the term formula.
Frequently asked questions
What is the correct answer to this question?
13
Why is this the correct answer?
Given \(a_n=10n+q\), we get \(a_{7n}=70n+q\) and \(a_{3n}=30n+q\). Hence, \(a_{7n}-a_{3n}=(70n+q)-(30n+q)=40n\). Therefore, \(40n=520\), so \(n=13\). The constant \(q\) cancels because it occurs in both terms. Exam tip: for terms such as \(a_{7n}\) and \(a_{3n}\), directly substitute \(7n\) and \(3n\) respectively in the term formula.
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.
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