If f(5) = 3.7 and f(6) = 8.7...
f(7) =
f(8) =
Recursive Function Is

f(7) = 13.7

f(8) = 18.7

Recursive Function Is: f(1) = -16.3; (fn) = f(n - 1) + 5

Step-by-step explanation:

The recursive function of the arithmetic sequence is

f(1) = first term; f(n) = f(n-1) + d, where

∵ f(5) = 3.7 and f(6) = 8.7

∵ d = f(6) - f(5)

∴ d = 8.7 - 3.7

∴ d = 5

∵ f(7) = f(6) + 5

∴ f(7) = 8.7 + 5

∴ f(7) = 13.7

∵ f(8) = f(7) + 5

∴ f(8) = 13.7 + 5

∴ f(8) = 18.7

→ To find f(1) subtract from each term the value of d

∵ f(5) = f(4) + d

∴ f(4) = f(5) - d

∴ f(4) = 3.7 - 5

∴ f(4) = -1.3

∵ f(3) = f(4) - 5

∴ f(3) = -1.3 - 5

∴ f(3) = -6.3

∵ f(2) = f(3) - 5

∴ f(2) = -6.3 - 5

∴ f(2) = -11.3

∵ f(1) = f(2) - 5

∴ f(1) = -11.3 - 5

∴ f(1) = -16.3

∴ Recursive Function Is: f(1) = -16.3; (fn) = f(n - 1) + 5