try it

1 5 9 19 49 101 181 (series is t)
4 14 30 52 80 114 (Series is s)
10 16 22 28 34 (series is a)

a_r = 10 + (n-1)6 = 6n-4
Σs_r = 4+14+30+52+80+...+s_n
Σs_r = 4 +14+30+52+...+s_n-1 + s_n
Subtracting, s_n = 4+10+16+...+(4+(n-1)6)
= n2(8+6n-2)
s_n = 3n(n+1) ... (i)
t_r+1 = t_r+s_r-1, r>1
So, t_r = t₂ + s₁ + s₂+s₃+...+s_r-2
= 5 + Σs_r (r=1 to r-2) which can easily be obtained from (i)

Now sum of n terms = 6 + Σt_r(r=3 to n-2)