Write a recursive formula for the geometric sequence 6, 9, 13.5, 20.25.

1. Divide the second term by the first: 9/6 = 1.5, so the common ratio is 1.5. 2. Confirm with the next pair: 13.5/9 = 1.5, so the ratio holds. 3. A recursive formula must also state the initial term, which is a_1 = 6. 4. The rule is therefore a_1 = 6 with a_n = 1.5 a_(n-1) for n >= 2. 5. Adding 3 each time would give 6, 9, 12, 15, which fails from the third term onwards. _Source: OpenStax Algebra and Trigonometry (CC BY 4.0), Ch 13 "Sequences, Probability and Counting Theory", section 13.3 Geometric Sequences_