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