If in an AP (a_3+a_9=72), what is the value of (a_6)?
Answer and explanation
Correct answer: 36
In an AP, the sum of terms equidistant from a middle term equals twice that middle term. Since the index 6 lies midway between 3 and 9, \(a_3+a_9=2a_6\). Thus, \(2a_6=72\), so \(a_6=36\). Values such as 34 or 38 would not give the stated sum of 72. Exam tip: use \(a_{m-r}+a_{m+r}=2a_m\) for symmetric terms in an AP.
Frequently asked questions
What is the correct answer to this question?
36
Why is this the correct answer?
In an AP, the sum of terms equidistant from a middle term equals twice that middle term. Since the index 6 lies midway between 3 and 9, \(a_3+a_9=2a_6\). Thus, \(2a_6=72\), so \(a_6=36\). Values such as 34 or 38 would not give the stated sum of 72. Exam tip: use \(a_{m-r}+a_{m+r}=2a_m\) for symmetric terms in an AP.
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.
