1. Problem: Given the sequence defined by the formula $$a_n=(-1)^n \cdot \frac{n+1}{2}$$ for each natural number $$n \geq 1$$, find the third term $$a_3$$. 2. Formula: The general term of the sequence is $$a_n=(-1)^n \cdot \frac{n+1}{2}$$. 3. Substitute $$n=3$$ into the formula: $$a_3=(-1)^3 \cdot \frac{3+1}{2}$$ 4. Calculate the power of $$-1$$: $$(-1)^3 = -1$$ 5. Calculate the fraction: $$\frac{3+1}{2} = \frac{4}{2} = 2$$ 6. Multiply the results: $$a_3 = -1 \cdot 2 = -2$$ 7. Conclusion: The third term of the sequence is $$-2$$, which corresponds to option B.