1. **State the problem:** We need to find the sum of the first 5 terms and the nth term of the geometric series 5 + 15 + 45 + 135 + ... 2. **Identify the series type and formula:** This is a geometric series where each term is multiplied by a common ratio $r$ to get the next term. 3. **Find the first term and common ratio:** - First term $a = 5$ - Common ratio $r = \frac{15}{5} = 3$ 4. **Formula for the nth term of a geometric series:** $$a_n = a \times r^{n-1}$$ 5. **Calculate the 5th term:** $$a_5 = 5 \times 3^{5-1} = 5 \times 3^4 = 5 \times 81 = 405$$ 6. **Formula for the sum of the first n terms of a geometric series:** $$S_n = a \times \frac{r^n - 1}{r - 1}$$ 7. **Calculate the sum of the first 5 terms:** $$S_5 = 5 \times \frac{3^5 - 1}{3 - 1} = 5 \times \frac{243 - 1}{2} = 5 \times \frac{242}{2} = 5 \times 121 = 605$$ **Final answers:** - The 5th term is $405$ - The sum of the first 5 terms is $605$