To represent a geometric sequence, we can use a function that describes the \( n \)-th term of the sequence. In this case, the sequence you provided is 6, 18, 54, ...
To determine the parameters of the geometric sequence:
- The first term \( a \) is 6.
- The common ratio \( r \) can be found by dividing the second term by the first term: \( r = \frac{18}{6} = 3 \).
The general formula for the \( n \)-th term of a geometric sequence can be written as:
\[ a_n = a \cdot r^{(n-1)} \]
where \( a \) is the first term and \( r \) is the common ratio.
Now, we can write this as a Python function:
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): # Get the first 5 terms
print(geometric_sequence(i))
This function, geometric_sequence(n), returns the \( n \)-th term of the geometric sequence defined by the first term 6 and a common ratio of 3. The example usage will print the first five terms of the sequence.
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