Write the next three terms of the following sequences:

for all

Given: t₁ = 3 and t_n = 3t_n-1 + 2

Now, we have to find next three terms i.e. t₂, t₃ and t₄

Taking n = 2, we get

t₂ = 3t_2-1 + 2

= 3t₁ + 2

= 3(3) + 2 [given: t₁ = 3]

t₃ = 9 + 2

t₃ = 11 …(i)

Taking n = 3, we get

t₃ = 3t_3-1 + 2

= 3t₂ + 2

= 3(11) + 2 [from (i)]

= 33 + 2

t₃ = 35 …(ii)

Taking n = 4, we get

t₄ = 3t_4-1 + 2

= 3t₃ + 2

= 3(35) +2

t₅ = 105 + 2

t₅ = 107 [from (ii)]

Hence, the next three terms are 11, 35 and 107.