No Free Butterflies

Same-expiry European calls on an airline stock trade at prices $c_1, c_2, c_3$ for strikes $K_1 < K_2 < K_3$, where the strikes are equally spaced: $K_3 - K_2 = K_2 - K_1$. Using only a no-arbitrage argument, show that $c_2 \le \frac{c_1 + c_3}{2}$, and state the corresponding inequality for European puts.