Unit 5 Study Guide Using this sequence: $$ 1,3,9,27,81,243 $$ s the sequence shown above a geometric or arithmetic sequer

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To determine whether the sequence $$ 1, 3, 9, 27, 81, 243 $$ is geometric or arithmetic, we need to analyze the differences and ratios between consecutive terms.

1. **Arithmetic Sequence**: In an arithmetic sequence, the difference between consecutive terms is constant. We can calculate the differences:
   - $$ 3 - 1 = 2 $$
   - $$ 9 - 3 = 6 $$
   - $$ 27 - 9 = 18 $$
   - $$ 81 - 27 = 54 $$
   - $$ 243 - 81 = 162 $$

The differences are $$ 2, 6, 18, 54, 162 $$, which are not constant. Therefore, the sequence is not arithmetic.

2. **Geometric Sequence**: In a geometric sequence, the ratio between consecutive terms is constant. We can calculate the ratios:
   - $$ \frac{3}{1} = 3 $$
   - $$ \frac{9}{3} = 3 $$
   - $$ \frac{27}{9} = 3 $$
   - $$ \frac{81}{27} = 3 $$
   - $$ \frac{243}{81} = 3 $$

The ratios are all equal to $$ 3 $$, which is constant. Therefore, the sequence is geometric.

### Conclusion:
The sequence $$ 1, 3, 9, 27, 81, 243 $$ is a geometric sequence with a common ratio of $$ 3 $$.
The sequence $$ 1, 3, 9, 27, 81, 243 $$ is a geometric sequence with a common ratio of $$ 3 $$.

Unit 5 Study Guide Using this sequence: \( 1,3,9,27,81,243 \) s the sequence shown above a geometric or arithmetic sequer

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