10s(n- 1)=a(n- 1)^2+5a(n- 1)+6

The two formulas are subtracted because Sn-S(n- 1)=an.

10an=an^2-a(n- 1)^2+5(an-a(n- 1))

Transposition 5 (an+a (n-1)) = an 2-a (n-1) 2.

Because both sides of the positive term sequence of an are truncated to an+a(n- 1)

an-a(n- 1)=5

An arithmetic series and tolerance d=5.

Meaning: a3 2 = a1* a15.

(a 1+2d)^2=a 1*(a 1+ 14d)

Because d=5 is easy to know.

a 1=2

Solve a general formula:

an=5n-3