In the following recursive strings, determine: (1) its first 6 terms; (2) a general non-recursive rule; (3) proof by induction that the general rule is valid.

(a) (b) (c) S S(1) = 3; S(n) = S(n 1), n > 2. S S(1) = 1; S(n) = (-1). S(n 1), n > 2. S S(1) = 3; S(n) = 2 S(n-1), n > 2. S S S(1) = 1; S(n) = 2 + Son - 1), n > 2. S( S(1) = 5; S(n) = 5 + 2. S(n 1), n > 2. (d) { (e)