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)

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

y=-2.5x+12.5

step-by-step explanation:

5y=2x+10

y=0.4x+2

slope=-2.5

5=-2.5*3+b

b=12.5