solve the recurrence Solve the recurrence C_n + 1 = C_n + 3(n + 1), C_0 = 17 Solution We have Cn+1 = Cn+3(n+1), so that Cn = Cn-1 +3n = Cn-2 + 3 (n-1) +3n = Cn-3 + 3(n-2)+ 3(n- 1)+3n. We can continue like this till we reach C1 = C0 + 3*1 = 17 +3*1 (as C0= 17). Now, we can conclude that Cn = 17+3*1 +3*2 +…+3*n = 17 + 3(1+2+…+n) = 17 + 3 [n(n+1)/2] ( as the sum of first n natural numbers is n(n+1)/2). Thus, Cn = 17 + 3 [n(n+1)/2].