If in an AP (a_{27}=a_8+171), what is the common difference?
Answer and explanation
Correct answer: 9
In an AP, the difference between two terms equals the difference of their positions multiplied by the common difference: \(a_{27}-a_8=(27-8)d=19d\). Given \(a_{27}-a_8=171\), we get \(19d=171\), so \(d=9\). Hence, option C is correct. If the common difference were 8, the term difference would be \(19\times8=152\), not 171. Exam tip: use \(a_m-a_n=(m-n)d\) to solve such questions quickly.
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 of their positions multiplied by the common difference: \(a_{27}-a_8=(27-8)d=19d\). Given \(a_{27}-a_8=171\), we get \(19d=171\), so \(d=9\). Hence, option C is correct. If the common difference were 8, the term difference would be \(19\times8=152\), not 171. Exam tip: use \(a_m-a_n=(m-n)d\) to solve such questions quickly.
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.
