A sequence is defined by the recursive function f (n + 1) = 1/3f (n). If f (3) = 9, what is f (1)

a) 1

b) 3

c) 27

d) 81

Means the next term is the previuos term times 1/3

f (n+1) = 1/3f (n)

times 3 both sides

3f (n+1) = f (n)

so

3f (3) = 3f (2+1) = f (2)

3f (3) = f (2)

3 (9) = f (2)

27=f (2)

3f (2) = 3f (1+1) = f (1)

3f (2) = f (1)

3 (27) = f (1)

81=f (1)

D is answer