Question 935569
THAT makes better sense.  Start at n=1, use the formula, and work forward.


{{{A[2]=A[1+1]=3*2+2=highlight(8)}}}



{{{A[3]=3*8+2=highlight(26)}}}



{{{A[4]=3*26+2=highlight(80)}}}


You find the next three terms.




You also wanted to find the explicit formula.
On paper, the process of composing the first few successive terms is messy.  I found for the fifth term, This:
{{{A[5]=2(3^4+3^3+3^2+3^1+3^0)}}}
I can guess, if this remains workable, that the pattern is apparent.  This seems to be based on the sum of a geometric sequence.  
...
Fifth term should be 242.
I would guess along the apparent formula that the sixth term would be 728.