How to find the first 5 values of a recursive relation where certain sequences are not known?

310 Views Asked by At

Write down the first five values of each of the following recursive sequences.

(a) r(0) = 2, r(n) = [r(n-1)] -n -1 for all integers n>=1 (I couldn't write the values as ace of r and s so I just wrote them in brackets; any edit would be appreciated)

(b) s(0) = 2, s(n) = [s(n-1)] + [s(n-2)] +......+ [s(0)]^2

Part a is pretty simplee and I got values r(1) = 2, r(2) = 1, r(3) = -3, r(4) = 4, r(5) = 10

I hope that is correct.

Part b am not really sure how I will do this. For n =1 I get s(1) = s(0)^2 +(-1)^2 +.....+s(0)^2

I have the value for s(0) = 2 but how do I get the value for s(-1) and the values in between s(n-2)^2 and s(0)^2?