Answer:
f(n) = 2n - 2
Step-by-step explanation:
Given the recursive formula
f(n) = f(n - 1) + 2 with f(1) = 0, then
f(2) = f(1) + 2 = 0 + 2 = 2
f(3) = f(2) + 2 = 2 + 2 = 4
f(4) = f(3) + 2 = 4 + 2 = 6
The terms of the sequence are 0, 2, 4, 6, ....
These are the first 4 terms of an arithmetic sequence with explicit formula
f(n) = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here d = 2 - 0 = 4 - 2 = 6 - 4 = 2 and a₁ = 0, thus
f(n) = 0 + 2(n - 1), that is
f(n) = 2n - 2 ← explicit formula
