Additionally, the boss asked Armando to determine how many toy sales branches he would have in the fifteenth year, knowing that the first year they started with two branches, by the second they already had 5 branches and, by the third year, they had 8 branches. From the above, determine the number of branches it will have for the fifteenth year.

We have the order 2,5,8 The sequence is an increment of 3: 2 2+3 = 5 5+3 = 8 So the sequence is $$ a_n=3n-1 $$ $$ a_1=3\left(1\right)-1=2 $$ $$ a_2=3\left(2\right)-1=5 $$$$ a_3=3\left(3\right)-1=8 $$ So, the number of branches in fifteenth year is: $$ a_{15}=3\left(15\right)-1=44 $$