Question

the first four terms of a geometric sequence are shown.
\\(\frac{1}{3}, 3, 27, 243, \dots\\)
complete the statement.
the recursive formula for the sequence is:
\\(a_1 = \boxed{}\\)
\\(a_n = a_{n - 1} \cdot \boxed{}\\)
\\(\boxed{9}\\) \\(\boxed{\frac{1}{3}}\\) \\(\boxed{1}\\) \\(\boxed{\frac{8}{3}}\\)

Explanation:

Step1: Identify first term

The first term $a_1$ is given as the first value in the sequence: $\frac{1}{3}$

Step2: Find common ratio $r$

Calculate ratio of term to prior term: $r = \frac{3}{\frac{1}{3}} = 9$

Step3: Define recursive formula

Recursive formula uses $a_1$ and $a_n = a_{n-1} \cdot r$

Answer:

$a_1 = \frac{1}{3}$
$a_n = a_{n-1} \cdot 9$