If in an AP (a_2=9) and (a_5+a_8=72), what is (a_{14})?
Answer and explanation
Correct answer: 81
In an AP, the difference between consecutive terms is constant. Since \(a_5=a_2+3d\) and \(a_8=a_2+6d\), we get \(9+3d+9+6d=72\). Thus, \(18+9d=72\), so \(d=6\). Now \(a_{14}=a_2+12d=9+12\times6=81\). Hence, 81 is correct. A value such as 73 may result from incorrectly counting the number of common differences between the terms. Exam tip: from \(a_r\) to \(a_s\), the change is \((s-r)d\).
Frequently asked questions
What is the correct answer to this question?
81
Why is this the correct answer?
In an AP, the difference between consecutive terms is constant. Since \(a_5=a_2+3d\) and \(a_8=a_2+6d\), we get \(9+3d+9+6d=72\). Thus, \(18+9d=72\), so \(d=6\). Now \(a_{14}=a_2+12d=9+12\times6=81\). Hence, 81 is correct. A value such as 73 may result from incorrectly counting the number of common differences between the terms. Exam tip: from \(a_r\) to \(a_s\), the change is \((s-r)d\).
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.
