In an AP, (a_{5n}=205), (a_n=49), and (d=13). What is (n)?
Answer and explanation
Correct answer: 3
In an AP, the difference between two terms equals the difference of their indices multiplied by the common difference. Thus, \(a_{5n}-a_n=(5n-n)d=4nd\). Hence \(205-49=4n\times13\), so \(156=52n\), giving \(n=3\). If \(n=4\), the difference would be \(208\), not 156. Exam tip: In such questions, subtract the given terms instead of first finding the initial term.
Frequently asked questions
What is the correct answer to this question?
3
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, \(a_{5n}-a_n=(5n-n)d=4nd\). Hence \(205-49=4n\times13\), so \(156=52n\), giving \(n=3\). If \(n=4\), the difference would be \(208\), not 156. Exam tip: In such questions, subtract the given terms instead of first finding the initial term.
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.
