For which \(s\) will \(\frac{s}{2}, s+3, 3s-1\) form an arithmetic progression?

Correct answer: \(\frac{14}{3}\)

In an arithmetic progression, the differences between consecutive terms are equal. The first difference is \((s+3)-\frac{s}{2}=\frac{s}{2}+3\), and the second is \((3s-1)-(s+3)=2s-4\). Thus, \(\frac{s}{2}+3=2s-4\), which gives \(s=\frac{14}{3}\). If \(s=8\), the two differences are not equal. Exam tip: For three terms in an AP, equate the first and second differences.