Write the first five terms of each of the sequences in and obtain the corresponding series:

a₁ = 3, a_n = 3a_{n – 1} + 2 for all n > 1

Given here are a₁ = 3,

a_n = 3a(_{n – 1)} + 2…………1

To find out first five terms of the sequence we will put value of n = 2, 3, 4, 5 in 1

a₂= 3(3)_2-1 + 2 = 3 × 3 + 2 = 11

a₃ = 3a₂ + 2 = 3 × 11 + 2 = 35 (∵ a_n-1 = a_3-1 = a₂ )

a₄ = 3a₃ + 2 = 105 + 2 = 107

a₅ = 3a₄ + 2 = 3 × 107 + 2 = 323

Hence the first five terms of the sequence are 3, 11, 35, 107, 323

And the corresponding sequence is 3 + 11 + 35 + 107 + 323 + …….