Three consecutive AP terms are (7,x,31). What are (x) and the common difference?

Correct answer: \(x=19,\ d=12\)

For three consecutive terms of an AP, the middle term is the average of the first and third terms. Hence, \(x=\frac{7+31}{2}=19\). The common difference is \(d=19-7=12\), and this is verified by \(31-19=12\). In option A, the difference from \(7\) to \(18\) is \(11\), but from \(18\) to \(31\) it is \(13\), so it is not an AP. Exam tip: for three consecutive AP terms, use \(2\times\text{middle term}=\text{first term}+\text{third term}\).