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.
-
Identify the first term: The first term \(c(1)\) is \(-15\).
-
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: \[ c(1) = -15 \] \[ c(n) = c(n-1) + 4 \]
1 answer