1. **State the problem:** We need to find the sum of the first 5 terms and the nth term of the geometric series 4, 8, 16, 32, ... 2. **Identify the series type and formula:** This is a geometric series where the first term $a = 4$ and the common ratio $r = \frac{8}{4} = 2$. 3. **Formula for the nth term:** $$a_n = a \times r^{n-1}$$ 4. **Calculate the nth term:** $$a_n = 4 \times 2^{n-1}$$ 5. **Formula for the sum of the first n terms:** $$S_n = a \times \frac{r^n - 1}{r - 1}$$ 6. **Calculate the sum of the first 5 terms:** $$S_5 = 4 \times \frac{2^5 - 1}{2 - 1} = 4 \times \frac{32 - 1}{1} = 4 \times 31 = 124$$ **Final answers:** - The nth term is $a_n = 4 \times 2^{n-1}$ - The sum of the first 5 terms is $124$