Answer: our sequence is f(n) = f(n-1) + 2
where f(1) = 6
Explanation:
An arithmetic sequence is a sequence where the difference between any two succesive terms is the same:
so here we have that:
f(1) = 6
f(4) = 12
f(7) = 18
we would have that:
f(2) - f(1) = c
f(3) - f(2) = c
f(4) - f(3) = c
then we can add those 3 equations and get:
(f(2) - f(1)) + (f(3) - f(2)) + (f(4) - f(3)) = c + c + c
f(4) - f(1) = 3c
12 - 6 = 3*c
6 = 3*c =
c = 6/3 = 2
now, then we must have that:
f(7) - f(4) = 3*c = 6
18 - 12 = 6
so this is consistent.
then our sequence is f(n) = f(n-1) + 2
where f(1) = 6