Answer:
f(n+1) = f(n) - 6
Step-by-step explanation:
Assume your sequence is
5, –1, –7, –13, –19, …
A recursive formula defines each term of a sequence using the preceding term.
For your sequence,
f(1) = 5
f(2) = -1
f(3) = -7
f(4) = -13
f(5) = -19
We see that
f(2) - f(1) = -1 - 5 = -6
f(3) - f(2) = -7 - (-1) = -6
f(4) - f(3) = -13 - (-7) = -6
f(5) - f(4) = -19 - (-13) = -6
Each term is six units less than the preceding term.
The repeating pattern (recursive formula) is
f(n + 1) - f(n) - 6 or
f(n+ 1) = f(n) - 6
