High School Pre-Cal

Question

Which recursive formula models the sequence below?

–1, 0, –1, 0, –1, 

 

 

 

Answer 1

 

   f(n) = f(n-1) - (-1)^(n-1)  

 

   f(1) = -1

 

  f(2) = f(1) - (-1)^(2-1) = -1 - (-1)^1 = -1 - (-1) = 0

 

f(3) = f(2) - (-1)^(3-1) = 0 - (-1)^2 = 0 - 1 = -1

 

f(4) = f(3) - (-1)^(4-1) = -1 - (-1)^3 = -1 - (-1) = 0

 

f(5) = f(4) - (-1)^(5-1) = 0 - (-1)^4 = 0 - 1 = -1

etc..