Final answer:
The recursive formula for the sequence {0.25, 0.75, 2.25, 6.75 …} is a_1 = 0.25, a_n = 3 × a_(n-1) for n > 1. This suggests that each term is obtained by multiplying the previous term by 3.
Step-by-step explanation:
The student has asked to write the recursive formula for the sequence {0.25, 0.75, 2.25, 6.75 …}. To determine the recursive formula, we should look for a pattern in the changes from one term to the next within the sequence.
Observing the sequence, each term is being multiplied by 3 to get the next term:
- 0.25 × 3 = 0.75
- 0.75 × 3 = 2.25
- 2.25 × 3 = 6.75
Thus, the recursive formula for this geometric sequence can be defined as:
a1 = 0.25
an = 3 × an-1 (for n > 1)
Where a1 is the first term and an is the n-th term of the sequence.