If in an AP (a_{18}=a_6+84), what is the common difference?
Answer and explanation
Correct answer: 7
In an AP, the difference between two terms equals the difference of their positions multiplied by the common difference. Thus, \(a_{18}-a_6=(18-6)d=12d\). Given \(a_{18}-a_6=84\), we get \(12d=84\), so \(d=7\). The option 6 may result from counting the position gap incorrectly. Exam tip: use \(a_m-a_n=(m-n)d\) and subtract the indices carefully.
Frequently asked questions
What is the correct answer to this question?
7
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. Thus, \(a_{18}-a_6=(18-6)d=12d\). Given \(a_{18}-a_6=84\), we get \(12d=84\), so \(d=7\). The option 6 may result from counting the position gap incorrectly. Exam tip: use \(a_m-a_n=(m-n)d\) and subtract the indices carefully.
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.
