If in an AP \(a_4+a_{14}=98\), what is the value of \(a_9\)?
Answer and explanation
Correct answer: 49
In an AP, the sum of two terms equally spaced from a middle term equals twice that middle term. Since \(\frac{4+14}{2}=9\), we have \(a_4+a_{14}=2a_9\). Thus \(2a_9=98\), so \(a_9=49\). Choosing \(51\) would make the sum \(102\), not \(98\). Exam tip: Find the average of the term indices to identify the middle term quickly.
Frequently asked questions
What is the correct answer to this question?
49
Why is this the correct answer?
In an AP, the sum of two terms equally spaced from a middle term equals twice that middle term. Since \(\frac{4+14}{2}=9\), we have \(a_4+a_{14}=2a_9\). Thus \(2a_9=98\), so \(a_9=49\). Choosing \(51\) would make the sum \(102\), not \(98\). Exam tip: Find the average of the term indices to identify the middle term 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.
