Question

Which sequence can be defined by the recursive formula f (1) = 4, f (n + 1) = f (n) – 1.25 for n ≥ 1?

Answer 1

4, 2.75, 1.5, 0.25, - 1, - 2.25, ...............

Explanation:

Using the recursive formula with f(1) = 4, then

f(2) = f(1) - 1.25 = 4 - 1.25 = 2.75

f(3) = f(2) - 1.25 = 2.75 - 1.25 = 1.5

f(4) = f(3) - 1.25 = 1.5 - 1.25 = 0.25

f(5) = f(4) - 1.25 = 0.25 - 1.25 = - 1

f(6) = f(5) - 1.25 = - 1 - 1.25 = - 2.25

Sequence is 4, 2.75, 1.5, 0.25, - 1, - 2.25, .......