Subjects algebra

Geometric Term 9993E4

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1. **State the problem:** We have a geometric sequence where the first term $a_1 = 6$ and the second term $a_2 = 18$. We need to find the 8th term $a_8$. 2. **Recall the formula for the $n$th term of a geometric sequence:** $$a_n = a_1 \times r^{n-1}$$ where $r$ is the common ratio. 3. **Find the common ratio $r$:** Since $a_2 = a_1 \times r$, we have $$18 = 6 \times r$$ Divide both sides by 6: $$\cancel{6} \times r = \frac{18}{\cancel{6}}$$ $$r = 3$$ 4. **Calculate the 8th term $a_8$:** $$a_8 = 6 \times 3^{8-1} = 6 \times 3^7$$ Calculate $3^7$: $$3^7 = 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 = 2187$$ So, $$a_8 = 6 \times 2187 = 13122$$ 5. **Final answer:** The 8th term is $\boxed{13122}$, which corresponds to option c.