If the first differences d_k = a_{k+1} - a_k form an AP, GP, or known sequence, then a_n = a_1 + sum(d_k, k=1 to n-1). If second differences are constant (quadratic sequence), the general term is quadratic: a_n = An^2 + Bn + C. Determine A, B, C from three known values. This is useful for finding the nth term of sequences defined by their partial sums or difference patterns.