Question

A sequence is defined by the recursive formula f (n + 1) = f(n) – 2. If f(1) = 18, what is f(5)?

Answer 1

$f(2)=18-2=16\\ f(3)=16-2=14\\ f(4)=14-2=12\\ \boxed{f(5)=12-2=10}$

Answer 2

For this case we have the following recursive formula:
 $f (n + 1) = f (n) - 2$
 What we must do in this case is to evaluate different values of n until we find f (5)
 We have then:
 For n = 1:
 $f (1 + 1) = f (1) - 2 f (2) = f (1) - 2 f (2) = 18 - 2 f (2) = 16$
 For n = 2:
 $f (2 + 1) = f (2) - 2 f (3) = f (2) - 2 f (3) = 16 - 2 f (3) = 14$
 For n = 3:
 $f (3 + 1) = f (3) - 2 f (4) = f (3) - 2 f (4) = 14 - 2 f (4) = 12$
 For n = 4:
 $f (4 + 1) = f (4) - 2 f (5) = f (4) - 2 f (5) = 12 - 2 f (5) = 10$
 Answer:
 The value of the recursive formula for f (5) is given by:
 $f (5) = 10$