Could someone please help me with this question and answer my written questions that are in ink

We define the sequence (Sn) recursively by letting s1 = 1 and Sn+1 = \\28n + 2. . Find lim Sn. s = lim Sn = lim Sn+ 1 = lim /2(sn) + 2 = lim (2(Sn) + 2) = lim (2(Sn)) + 2 by Theorem 4.2. 1(b) = 2 . lim (Sn) + 2 by Theorem 4.2. 1(b) = V2s + 2 since lim (Sn) = s $2 = 2s + 2 by squaring both sides of the equation S' - 25 - 2 = 0 ( - 2) 2 - 4(1) ( - 2) S = - -21 by the quadratic formula 2(1) should This be !? If so V12 why ? 2 = 2+ 13 - So lim Sn = ? ? and why