Complete the recursive formula of the arithmetic sequence

To complete the recursive formula for the given arithmetic sequence \(-15, -11, -7, -3, \ldots\), we need to identify the first term and the common difference.

1. **Identify the first term**:
The first term \(c(1)\) is \(-15\).

2. **Calculate the common difference**:
To find the common difference, subtract the first term from the second term:
\[
-11 - (-15) = -11 + 15 = 4
\]
We can confirm this by checking the other successive terms:
\[
-7 - (-11) = -7 + 11 = 4
\]
\[
-3 - (-7) = -3 + 7 = 4
\]
Hence, the common difference \(d\) is 4.

Putting this together, we can complete the recursive formula:

- The first term is:
\[
c(1) = -15
\]

- The recursive formula for subsequent terms is:
\[
c(n) = c(n-1) + 4
\]

So the final completed recursive formula is:
\[
c(1) = -15
\]
\[
c(n) = c(n-1) + 4
\]