We have given a1 = 3 , an = 3an−1 + 2
⇒ a1 = 3, a2 = 3a1 + 2 = 3·3 + 2 = 9 + 2 = 11,
a3 = 3a2 + 2 = 3·11 + 2 = 33 + 2 = 35,
a4 = 3a3 + 2 = 3 ·35 + 2 = 105 + 2 = 107,
a5 = 3a4 + 2 = 3·107 + 2 = 321 + 2 = 323
Hence the first five terms of the sequence are 3, 11, 35, 107, 323.
The corresponding series is 3 + 11 + 35 + 107 + 323 +.......