Question

Explicit and Recursive Functions:

Write the explicit function that can be used to determine the number of seats in the nth row of the amphitheater. The function should be in the form f(n) = an + b, where a and b are integers.

Answer 1

In this problem we need to find the value of a and b. So given that the function should be in the form f(n) = an + b and we know each value of n, then out goal is to find a and b.

For getting this purpose, we need to find a system of two equations (given that we have two unknown variables)

Therefore:

(1) f(0) = a(1) + b = 18
∴ a + b = 18

(2) f(1) = a(2) + b = 24
∴ 2a + b = 24

Solving for a and b we have:

a = 6
b = 12

Finally:

f(n) = 6n + 12