If (a_n=5n+q) and (a_{4n}-a_n=135), what is the value of (n)?
Answer and explanation
Correct answer: 9
Given \(a_n=5n+q\), we have \(a_{4n}=5(4n)+q=20n+q\). Hence, \(a_{4n}-a_n=(20n+q)-(5n+q)=15n\). Since \(15n=135\), \(n=9\). Therefore, option C is correct. The constant \(q\) cancels because it occurs in both terms. Exam tip: substitute the given indices into the term formula first, then simplify the difference.
Frequently asked questions
What is the correct answer to this question?
9
Why is this the correct answer?
Given \(a_n=5n+q\), we have \(a_{4n}=5(4n)+q=20n+q\). Hence, \(a_{4n}-a_n=(20n+q)-(5n+q)=15n\). Since \(15n=135\), \(n=9\). Therefore, option C is correct. The constant \(q\) cancels because it occurs in both terms. Exam tip: substitute the given indices into the term formula first, then simplify 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.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
