According to Molecular Orbital Theory, the bond order is calculated as $\frac{1}{2} (N_b - N_a)$, where $N_b$ is the number of bonding electrons and $N_a$ is the number of antibonding electrons.

• $\text{O}_2$: has 16 electrons. Its configuration is $\sigma 1s^2 \sigma^* 1s^2 \sigma 2s^2 \sigma^* 2s^2 \sigma 2p_z^2 (\pi 2p_x^2 = \pi 2p_y^2) (\pi^* 2p_x^1 = \pi^* 2p_y^1)$. Bond order = $\frac{10 - 6}{2} = 2.0$.
• $\text{O}_2^+$: has 15 electrons (one electron removed from the antibonding $\pi^*$ orbital). Bond order = $\frac{10 - 5}{2} = 2.5$.
• $\text{O}_2^{2+}$: has 14 electrons (two electrons removed from the antibonding $\pi^*$ orbitals). Bond order = $\frac{10 - 4}{2} = 3.0$.
• $\text{O}_2^-$: has 17 electrons (one electron added to the antibonding $\pi^*$ orbital). Bond order = $\frac{10 - 7}{2} = 1.5$. Therefore, the correct decreasing sequence for bond order is $\text{O}_2^{2+} (3.0) > \text{O}_2^+ (2.5) > \text{O}_2^- (1.5)$.