To find the explicit formula for an arithmetic sequence, we first need to determine the first term and the common difference between the terms.
The terms provided are: 75, 9, 105, 12. However, it seems like these numbers are not consistently in an arithmetic sequence as they do not have a common difference. Let’s examine them:
- From 75 to 9, the difference is -66.
- From 9 to 105, the difference is +96.
- From 105 to 12, the difference is -93.
Since the differences are not the same, we cannot define them as a typical arithmetic sequence. In an arithmetic sequence, the difference between consecutive terms must remain constant.
If the sequence were correctly defined or if there was a mistake in interpreting the numbers, please clarify. However, based on the provided numbers, there is no explicit formula that represents these as an arithmetic sequence.