Find the first 4 terms of the recursively defined sequence w

Find the first 4 terms of the recursively defined sequence with a_1 = 4 and a_n+1 = 3a_n + 2.

Solution

a₁=4 , a_n+1=3a_n+2

when n=1

a₂=3a₁+4 =3(4)+2=14

when n=2

a₃=3(14)+2=44

when n=3

a₄=3(44)+2=134

when n=4

a₅=3(134)+2=404

4,14,44,134,404