Please show your work and simplify your final answer as much as possible. Please don't copy and paste a previously answered question.

Given the sequence defined with the recurrence relation:

d$\_0=2$

$d_k=3d_{k-1}+2k($for all integers $k$ greater than or equal to $1)$

Calculate the value for $d_1,d_2,d_3,d_4.$ Keeping the intermediate steps will help find the pattern and solve for the next part.

Using iteration, solve the recurrence relation when $n0($i$.$e$.$ find an analytic formula for d$\_$n$).$ In particular, your final answer should not contain $$ and $.$ You should not use any non$-$arithmetic operations like ceil, floor, round, or any if structure.