Step 1 :The difference between the second and first term is $\frac{p}{2}-1 - \frac{4}{3}p - 2$. The difference between the third and second term is $\frac{4}{3}p - 2 - \frac{p}{2} + 1$.
Step 2 :Setting these two expressions equal to each other gives us an equation in terms of p: $-0.833333333333333*p - 3 = 0.833333333333333*p - 1$
Step 3 :Solving this equation gives us the value of p: $p = -1.2$
Step 4 :Final Answer: \(\boxed{-1.2}\)