If in an AP (a_4=20) and (a_9+a_{14}=160), what is (a_{28})?
Answer and explanation
Correct answer: 212
In an AP, the common difference is the same between consecutive terms. Here, \(a_9=a_4+5d\) and \(a_{14}=a_4+10d\). Therefore, \(20+5d+20+10d=160\), so \(15d=120\) and \(d=8\). Now, \(a_{28}=a_4+24d=20+24\times8=212\). Hence, 212 is correct. The value 204 does not result when the correct common difference \(d=8\) is used. Exam tip: when one term \(a_r\) is known, use \(a_n=a_r+(n-r)d\) directly.
Frequently asked questions
What is the correct answer to this question?
212
Why is this the correct answer?
In an AP, the common difference is the same between consecutive terms. Here, \(a_9=a_4+5d\) and \(a_{14}=a_4+10d\). Therefore, \(20+5d+20+10d=160\), so \(15d=120\) and \(d=8\). Now, \(a_{28}=a_4+24d=20+24\times8=212\). Hence, 212 is correct. The value 204 does not result when the correct common difference \(d=8\) is used. Exam tip: when one term \(a_r\) is known, use \(a_n=a_r+(n-r)d\) directly.
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.
