Suppose you have a sequence that begins {0, 1, 5, 21}. Give the next 3 numbers in your sequence. Use a recursive definition to define your sequence.

Question

Need help solving

Answer 1

It is 4 times the previous term plus 1

 

THe first term is 0

 

THe second term is 4(0)+1 = 0 + 1 = 1

 

The third term is 4(1)+1 = 4+1 = 5

 

The fourth term is 4(5)+1 = 20+1 = 21

 

The next 3 terms are 85, 341, 1365

 

The recursive function is F(n) = 4*F(n-1)+1  where F(0) = 0 and n=1,2,3,4,5