Answer:
f(n + 1) = f(n) + 2
Step-by-step explanation:
A recursive formula gives any term in the sequence from the previous term.
the n th term of an arithmetic sequence is
f(n) = f(1) + (n - 1)d ← d is the common difference
Given
f(1) = 6 and
f(4) = 12, then
f(1) + 3d = 12, that is
6 + 3d = 12 ( subtract 6 from both sides )
3d = 6 ( divide both sides by 3 )
d = 2
To obtain a term in the sequence add 2 to the previous term, hence
f(n + 1) = f(n) + 2 ← recursive formula
