1. **Stating the problem:** We are given a sequence defined by the first two terms and a recurrence relation: $$t_1 = 2, \quad t_2 = 4, \quad t_n = t_{n-1} + \frac{1}{2} t_{n-2}$$ We need to find the first 4 terms of this sequence. 2. **Understanding the recurrence:** Each term from the third onward is calculated by adding the previous term and half of the term before that. 3. **Calculate the third term:** $$t_3 = t_2 + \frac{1}{2} t_1 = 4 + \frac{1}{2} \times 2 = 4 + 1 = 5$$ 4. **Calculate the fourth term:** $$t_4 = t_3 + \frac{1}{2} t_2 = 5 + \frac{1}{2} \times 4 = 5 + 2 = 7$$ 5. **Summary of the first 4 terms:** $$t_1 = 2, \quad t_2 = 4, \quad t_3 = 5, \quad t_4 = 7$$ These are the first four terms of the sequence.