Subjects algebra

Geometric Sequence 89Faa9

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1. **State the problem:** Find the 8th term of the geometric sequence 8, 16, 32, ... 2. **Identify the first term and common ratio:** The first term $a_1 = 8$. The common ratio $r$ is found by dividing the second term by the first term: $$r = \frac{16}{8} = 2$$ 3. **Formula for the $n$th term of a geometric sequence:** $$a_n = a_1 \times r^{n-1}$$ 4. **Apply the formula to find the 8th term:** $$a_8 = 8 \times 2^{8-1} = 8 \times 2^7$$ 5. **Calculate $2^7$:** $$2^7 = 128$$ 6. **Multiply to get the 8th term:** $$a_8 = 8 \times 128 = 1024$$ **Final answer:** The 8th term of the sequence is $1024$.