Question

Write the first five terms of the following sequence and obtain the corresponding series:

a₁ = 3, a_n = 3a_{(n - 1)} + 2 for all n > 1

Answer 1

a_n = 3a_n−1 + 2 और a₁ = 3

Putting n = 2, 3, 4, 5 in the sequence,

a₂ = 3a₁ + 2

= 3 × 3 + 2

= 11

a₃ = 3a₂ + 2 

= 3 × 11+ 2

= 35

a₄ = 3a₃ + 2 

= 3 × 35 + 2

= 107

a₅ = 3a₄ + 2

= 3 × 107 + 2

= 323 

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

The corresponding series is 3 + 11 + 35 + 107 + 323 +...