a0 = 5

a1 = a0 + 1*2

a2 = a1 + 2*2

a3 = a2 + 3*2

a4 = a3 + 4*2

a5 = a4 + 5*2

.

.

.

an-1 = an-2 + (n - 1)*2

an = an-1 + n*2

Lets sum up he left sides and the right sides of the equations:

a0 + a1 + ... + an = 5 + a0 + ... + an-1 + 2(1 + 2 + ...+ n)

S = a0 + a1 + ... + an

S = 5 + S - an + 2*(n/2)(1 + n)

an = 5 + n(n + 1)

The sum of the first 30 terms is:

5 + 1*2 + 5 + 2*3 + 5 + 3*4 + .... + 5 + 30*31 =

= 5*30 + 1*2 + 2*3 + ...+29*30 + 30*31 = 150 + 9920 = 10,070.