3. Use iteration to guess an explicit formula for the sequence: t = t-1 + 7k+ 4k + 5, for all integers k 2 1, where to = 2 (using the formulas from Summation Properties Formulae.pdf & to simplify your answers whenever possible).Answer to Problem 3 Use iteration to guess an explicit formula for the sequence- to = th-1 + 3k + 1, for all integers k2 1, where to = 0. to = 0 ti=to+3 . 1+1=0+3 . 1+1=3 . 1+1 tz=ti+ 3 . 2+1 = (3 . 1+1)+3 - 2+1 =3 . (1+2) + 2 ta=tz+3 . 3+1 = (3 . (1+2)+2)+3 . 3+1 =3 . (1+2+3)+3 ta= t: + 3 . 4+1 = (3 . (1+2+3) +3) +3 . 4+1 =3 . (1 + 2 + 3 +4) + 4 Guess: to =3 . (1+2+3+ +(n-1)+n)+n n(n + 1) n n(n + 1) =3 . 2 +n [by the formula, k = K=1 2 3n- + 3n + 2n = by algebra 2 3n2 + 5n = (Ans) 2