Question

20. If a sequence is defined recursively by f(0) = 5 and

f(n + 1) = -3f(n) + 2 for n > 0, then f(3) is equal to

(1) 337
(3) 113
(2) -13
(4) -121

Answer 1

- 121

Explanation:

The recursive formula allows us to find the next term in a sequence from the previous term, thus

f(1) = - 3f(0) + 2 = - 3 × 5 + 2 = - 15 + 2 = - 13

f(2) = - 3f(1) = - 3 × - 13 + 2 = 39 + 2 = 41

f(3) = - 3f(2) + 2 = - 3 × 41 + 2 = - 123 + 2 = - 121