Nth term from quadratic sum

If the sum of the first $n$ terms of a series is $S_n=a+bn+c{n}^2$, find an expression for the $n^{\text{th}}$ term and describe the nature of the series.

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. VI. Harmonical Progression, Examples VI.a, No. 18