1. **State the problem:** We need to find the sum of all terms in a geometric series where the first term $a_1=4$ and the second term $a_2=-3$. 2. **Recall the formula for the sum of an infinite geometric series:** $$S = \frac{a_1}{1 - r}$$ where $r$ is the common ratio and $|r| < 1$ for the sum to exist. 3. **Find the common ratio $r$:** $$r = \frac{a_2}{a_1} = \frac{-3}{4} = -\frac{3}{4}$$ 4. **Check if $|r| < 1$:** $$\left| -\frac{3}{4} \right| = \frac{3}{4} < 1$$ So the sum formula applies. 5. **Calculate the sum:** $$S = \frac{4}{1 - \left(-\frac{3}{4}\right)} = \frac{4}{1 + \frac{3}{4}} = \frac{4}{\frac{7}{4}}$$ 6. **Simplify the fraction:** $$S = 4 \times \frac{4}{7} = \frac{16}{7}$$ **Final answer:** The sum of all terms in the series is $\frac{16}{7}$. Therefore, the correct choice is **b. 16 / 7**.