The recursive equation for t(n)=4.5n-8

t(1) = -3.5, Recursive equation is t(n) = t(n-1) + 4.5

Step-by-step explanation:

t(n)=4.5n-8

Let find the sequence

Plug in n=1,2,3,4

n=1      t(1)=4.5(1) -8= -3.5

n=2      t(2)=4.5(2) -8= 1

n=3      t(3)=4.5(3) -8= 5.5

n=4      t(4)=4.5(4) -8= 10

so sequence is -3.5, 1, 5.5, 10

Now we find the common difference

1 - (-3.5) = 4.5

5.5-1 = 4.5

10 - 5.5 = 4.5

common difference d = 4.5

Formula for recursive function is

t(n) = t(n-1) + d

We got d= 4.5

t(n) = t(n-1) + 4.5 , also t(1) = -3.5