To determine the next term in the sequence defined by the recursive formula [tex]\( f(n+1) = f(n) + 3 \)[/tex], given that the first term [tex]\( f(1) \)[/tex] is [tex]\(-4\)[/tex], follow these steps:
1. Identify the first term: The initial term [tex]\( f(1) \)[/tex] is given as [tex]\(-4\)[/tex].
2. Apply the recursive formula: According to the recursive formula [tex]\( f(n+1) = f(n) + 3 \)[/tex]:
- For [tex]\( n = 1 \)[/tex], [tex]\( f(2) = f(1) + 3 \)[/tex].
3. Calculate the next term:
- Substitute [tex]\( f(1) = -4 \)[/tex] into the formula.
- Therefore, [tex]\( f(2) = -4 + 3 \)[/tex].
4. Perform the arithmetic operation:
- [tex]\( -4 + 3 = -1 \)[/tex].
5. Determine the next term:
- The next term [tex]\( f(2) \)[/tex] is [tex]\(-1\)[/tex].
Thus, the next term in the sequence is [tex]\(\boxed{-1}\)[/tex].
