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.