1. **Problem:** If $p-1$, $p+1$, and $2p+3$ are in arithmetic progression (A.P.), find the value of $p$. 2. **Formula:** In an A.P., the middle term is the average of the first and third terms. So, $$p+1 = \frac{(p-1) + (2p+3)}{2}$$ 3. **Work:** $$p+1 = \frac{p-1 + 2p + 3}{2} = \frac{3p + 2}{2}$$ Multiply both sides by 2: $$2(p+1) = 3p + 2$$ $$2p + 2 = 3p + 2$$ Subtract $2p$ and 2 from both sides: $$0 = p$$ 4. **Answer:** $p = 0$. This corresponds to option (c).