1. **Problem:** Find the terms of the sequence $\{a_n\}$ where $a_n = 2 \cdot (-3)^n + 5^n$ for the following values: a) $a_0$, b) $a_1$, c) $a_4$, d) $a_5$. 2. **Formula:** The general term is given by $$a_n = 2 \cdot (-3)^n + 5^n$$ 3. **Step-by-step solution:** 1. Calculate $a_0$: $$a_0 = 2 \cdot (-3)^0 + 5^0 = 2 \cdot 1 + 1 = 2 + 1 = 3$$ 2. Calculate $a_1$: $$a_1 = 2 \cdot (-3)^1 + 5^1 = 2 \cdot (-3) + 5 = -6 + 5 = -1$$ 3. Calculate $a_4$: $$a_4 = 2 \cdot (-3)^4 + 5^4 = 2 \cdot 81 + 625 = 162 + 625 = 787$$ 4. Calculate $a_5$: $$a_5 = 2 \cdot (-3)^5 + 5^5 = 2 \cdot (-243) + 3125 = -486 + 3125 = 2639$$ **Final answers:** - a) $a_0 = 3$ - b) $a_1 = -1$ - c) $a_4 = 787$ - d) $a_5 = 2639$