Question

for the following geometric sequence: -1, -3, -9, -27, ... complete the recursive formula: f(n) = f(n - 1) · r

Explanation:

Step1: Find common ratio $r$

$r = \frac{f(2)}{f(1)} = \frac{-3}{-1} = 3$

Step2: Identify initial term

$f(1) = -1$

Step3: Define full recursive formula

Recursive formulas need the first term and the ratio relation.

Answer:

$f(1) = -1$, and for $n \geq 2$, $f(n) = f(n-1) \cdot 3$