\begin{tabular}{l} Question \ Use a geometric sequence to write the following as a fraction of integers. \ \hline Provide your answer below: \ \hline $$ 1.5 \overline{7} $$ \ \hline\end{tabular}

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UpStudy AI · Accepted Answer

To express the repeating decimal $$1.5\overline{7}$$ as a fraction of integers using a geometric sequence, we can follow these steps:

1. Let $$x = 1.5\overline{7}$$.
2. Multiply both sides of the equation by 10 to shift the decimal point one place to the right: $$10x = 15.7\overline{7}$$.
3. Subtract the original equation from the new equation to eliminate the repeating part: $$10x - x = 15.7\overline{7} - 1.5\overline{7}$$.
4. Simplify the subtraction to find the value of $$x$$.

Let's perform these steps to find the fraction equivalent of $$1.5\overline{7}$$.
Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$10x-x=15.7\overline{7}-1.5\overline{7}$$
- step1: Subtract the terms:
  $$9x=\frac{71}{5}$$
- step2: Multiply by the reciprocal:
  $$9x	imes \frac{1}{9}=\frac{71}{5}	imes \frac{1}{9}$$
- step3: Multiply:
  $$x=\frac{71}{45}$$
The fraction equivalent of $$1.5\overline{7}$$ is $$\frac{71}{45}$$.
The fraction equivalent of $$1.5\overline{7}$$ is $$\frac{71}{45}$$.

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Use a geometric sequence to write the following as a fraction of integers.

Provide your answer below:

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Question Use a geometric sequence to write the following as a fraction of integers. Provide your answer below: