Question

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

Answer 1

Answer:

a = 6

tn = a + (n - 1)d

t4 = 6 + 3d = 12

3d = 12 - 6 = 6

d = 6/3 = 2

f(n + 1) = f(n) + 2

Step-by-step explanation:

Answer 2

Answer: our sequence is f(n) = f(n-1) + 2

where f(1) = 6

Step-by-step 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