You already have the explicit rule for the sequence,
[tex]a_k=3+(k-1)1.5[/tex]
Simplify this a bit to get
[tex]a_k=3+1.5k-1.5=1.5+1.5k[/tex]
The series that sums these 6 terms is then
[tex]\displaystyle\sum_{k=1}^6a_k=\sum_{k=1}^6(1.5+1.5k)[/tex]
