1. **State the problem:** Find the 7th term of the geometric progression (GP) with first three terms 2, -10, 50, ... 2. **Recall the formula for the nth term of a GP:** $$a_n = a_1 \times r^{n-1}$$ where $a_1$ is the first term and $r$ is the common ratio. 3. **Find the common ratio $r$:** $$r = \frac{a_2}{a_1} = \frac{-10}{2} = -5$$ 4. **Verify the ratio with the third term:** $$a_3 = a_1 \times r^{2} = 2 \times (-5)^2 = 2 \times 25 = 50$$ This matches the given third term, so $r = -5$ is correct. 5. **Calculate the 7th term:** $$a_7 = 2 \times (-5)^{6}$$ 6. **Evaluate $(-5)^6$:** Since the exponent is even, $(-5)^6 = 5^6 = 15625$ 7. **Final calculation:** $$a_7 = 2 \times 15625 = 31250$$ **Answer:** The 7th term of the geometric progression is $31250$.