If in an AP (a_{31}=a_9+198), what is the common difference?
Answer and explanation
Correct answer: 9
In an AP, the difference between two terms equals the difference in their positions multiplied by the common difference. Thus, \(a_{31}-a_9=(31-9)d=22d\). Given \(a_{31}-a_9=198\), we get \(22d=198\), so \(d=9\). Hence, 9 is the correct option. If \(d=8\), the difference would be \(22\times8=176\), not 198. Exam tip: Use \(a_m-a_n=(m-n)d\) for direct questions of this type.
Frequently asked questions
What is the correct answer to this question?
9
Why is this the correct answer?
In an AP, the difference between two terms equals the difference in their positions multiplied by the common difference. Thus, \(a_{31}-a_9=(31-9)d=22d\). Given \(a_{31}-a_9=198\), we get \(22d=198\), so \(d=9\). Hence, 9 is the correct option. If \(d=8\), the difference would be \(22\times8=176\), not 198. Exam tip: Use \(a_m-a_n=(m-n)d\) for direct questions of this type.
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.
