1. **State the problem:** We have a geometric sequence with terms given for $n=1,3,6$ as 2, 50, and 6250 respectively. We need to find the 8th term. 2. **Recall the formula for the $n^{th}$ term of a geometric sequence:** $$a_n = a_1 \times r^{n-1}$$ where $a_1$ is the first term and $r$ is the common ratio. 3. **Use the given terms to find $r$:** From $n=1$, $a_1 = 2$. From $n=3$, $$a_3 = a_1 \times r^{3-1} = 2r^2 = 50$$ Solve for $r^2$: $$r^2 = \frac{50}{2} = 25$$ So, $$r = \pm 5$$ 4. **Check with $n=6$ term to determine the correct sign of $r$:** $$a_6 = a_1 \times r^{6-1} = 2r^5 = 6250$$ Substitute $r=5$: $$2 \times 5^5 = 2 \times 3125 = 6250$$ This matches the given term, so $r=5$. 5. **Find the 8th term:** $$a_8 = 2 \times 5^{7} = 2 \times 78125 = 156250$$ --- 6. **Second problem:** Find the value of $0.3 - 6a$ when $a = |1.2|$. 7. **Calculate $|1.2|$:** $$|1.2| = 1.2$$ 8. **Substitute into the expression:** $$0.3 - 6 \times 1.2 = 0.3 - 7.2$$ 9. **Simplify:** $$0.3 - 7.2 = -6.9$$ **Final answers:** - The 8th term of the geometric sequence is **156250**. - The value of $0.3 - 6a$ when $a=|1.2|$ is **-6.9**.