If f ( 1 ) = 1 f(1)=1 and f ( n ) = − 3 f ( n − 1 ) f(n)=−3f(n−1) then find the value of f ( 5 ) f(5).

Answer 1

This is a geometric series with a=f(1)=1 and r=-3

f(n)=f(1)(-3)^n-1

^{You plug in n=5 to get the answer.}

Answer 2

n = 2; f(2) = - 3f(1) = - 3;

n = 3, f(3) = - 3f(2) = 9;

n = 4, f(4) = - 3f(3) = - 27,

n = 5, f(5) = - 3f(4) = 81

But you can consider it as geometric series with a₁ = 1 and r = - 3