In an AP, (a_{6n}=319), (a_{2n}=95), and (d=14). What is (n)?
Answer and explanation
Correct answer: 4
In an AP, the difference between two terms equals the difference of their indices multiplied by the common difference. Thus, \(a_{6n}-a_{2n}=(6n-2n)d=4n\times14=56n\). Given \(319-95=224\), we get \(56n=224\), so \(n=4\). Therefore, option 4 is correct. Exam tip: subtract the given terms to eliminate the first term; there is no need to find it separately.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
In an AP, the difference between two terms equals the difference of their indices multiplied by the common difference. Thus, \(a_{6n}-a_{2n}=(6n-2n)d=4n\times14=56n\). Given \(319-95=224\), we get \(56n=224\), so \(n=4\). Therefore, option 4 is correct. Exam tip: subtract the given terms to eliminate the first term; there is no need to find it separately.
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.
