To complete the recursive formula for the given arithmetic sequence \(12, 10, 8, 6, \ldots\), we first observe that this sequence has a common difference.
The difference between each term is:
- \(10 - 12 = -2\)
- \(8 - 10 = -2\)
- \(6 - 8 = -2\)
So, the common difference (\(d\)) is \(-2\).
Now we can define the recursive formula:
- The first term of the sequence (\(b(1)\)) is 12.
- Each term can be expressed as the previous term plus the common difference.
Therefore, we can write the recursive formula as:
- \(b(1) = 12\)
- \(b(n) = b(n - 1) - 2\) for \(n > 1\)
In summary:
- \(b(1) = 12\)
- \(b(n) = b(n - 1) - 2\) for \(n > 1\)