Write a function to represent the geometric sequence 6, 18, 54

1 answer

To represent the geometric sequence 6, 18, 54, we can define a function that computes the \(n\)th term of the sequence. A geometric sequence can be represented by the formula:

\[ a_n = a_1 \cdot r^{(n-1)} \]

Where:

  • \(a_n\) is the \(n\)th term of the sequence
  • \(a_1\) is the first term of the sequence
  • \(r\) is the common ratio
  • \(n\) is the term number

In your sequence:

  • The first term \(a_1 = 6\)
  • The common ratio \(r\) can be calculated by dividing any term by the previous term. For instance, \(r = 18 / 6 = 3\).

So, the \(n\)th term of the sequence is given by:

\[ a_n = 6 \cdot 3^{(n-1)} \]

Now, here's a function in Python to represent this geometric sequence:

def geometric_sequence(n):
    a1 = 6  # first term
    r = 3   # common ratio
    an = a1 * (r ** (n - 1))  # n-th term formula
    return an

# Example usage:
for i in range(1, 4):
    print(geometric_sequence(i))  # Output: 6, 18, 54

This function geometric_sequence(n) calculates the \(n\)th term of the geometric sequence. In the loop provided as an example, n varies from 1 to 3, yielding the terms 6, 18, and 54.