Write an explicit rule for the sequence given the information below.

Question

f(1) = 1/2

f(n)= -6f(n-1)

Answer 1

Given recursive formula: f(n) =-6f(n-1), f(1)=1/2

f(1) = 1/2

f(2) = -6(1/2)

f(3) = = -6((1/2)(-6))=(1/2)(-6)²

f(4) = -6((1/2)(-6)²)=(1/2)(-6)³

f(5) = -6((1/2)(-6)³) = (1/2)(-6)⁴

...

f(n) = (1/2)(-6)^n-1