Question

Write a function to represent the geometric sequence 6, 18, 54, . . . .(1 point)

Answer 1

To represent the geometric sequence 6, 18, 54, ..., we can identify that this sequence has a first term \( a = 6 \) and a common ratio \( r = 3 \) (since \( 18 / 6 = 3 \) and \( 54 / 18 = 3 \)).

A function that generates the \( n \)-th term of this geometric sequence can be defined as follows:

### Python Function

```python
def geometric_sequence(n):
a = 6 # First term
r = 3 # Common ratio
return a * (r ** (n - 1))

# Example usage
for i in range(1, 6):
print(geometric_sequence(i))
```

### Explanation
- The function `geometric_sequence(n)` calculates the \( n \)-th term of the sequence using the formula for the \( n \)-th term of a geometric sequence:

\[
a_n = a \cdot r^{(n-1)}
\]

- Here, \( a \) is the first term (6) and \( r \) is the common ratio (3).
- The `for` loop at the end demonstrates how to generate the first 5 terms of the sequence.

### Output
This will output:
```
6
18
54
162
486
```

These are the first 5 terms of the geometric sequence.