In an AP, (a_{7n}=530), (a_{3n}=146), and (d=16). What is (n)?
Answer and explanation
Correct answer: 6
In an AP, the difference between two terms equals the difference of their indices multiplied by the common difference. Thus, \(a_{7n}-a_{3n}=(7n-3n)d=4n\times16\). Hence \(530-146=64n\), so \(384=64n\), giving \(n=6\). If 5 were used, the difference between the terms would be \(320\), not \(384\). Exam tip: subtract the two given terms directly; there is no need to find the first term.
Frequently asked questions
What is the correct answer to this question?
6
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, \(a_{7n}-a_{3n}=(7n-3n)d=4n\times16\). Hence \(530-146=64n\), so \(384=64n\), giving \(n=6\). If 5 were used, the difference between the terms would be \(320\), not \(384\). Exam tip: subtract the two given terms directly; there is no need to find the first 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.
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