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A sequence is defined recursively by the formula [tex]f(n+1) = f(n) + 3[/tex]. The first term of the sequence is -4.

What is the next term in the sequence?

Sagot :

GinnyAnsweridn
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].
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