Three terms of an arithmetic sequence are shown below. Which recursive formula defines the sequence? f (1) = 6, f (4) = 12, f (7) = 18 f (n + 1) = f (n) + 6 f (n + 1) = 2f (n) f (n + 1) = f (n) + 2 f (n + 1) = 1.5f (n)

c

Step-by-step explanation:

its c

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