When a sequence's general term isn't obvious, compute differences. If first differences $d_k$=$a_{k+1}$-$a_k$ form an AP, the sequence is quadratic: $a_n$=$An^{2+Bn+C}$. If differences form a GP, sum the geometric series. For partial sums: if $S_n$ is given, then $a_n$=S_{n-S}_{n-1} (for n>=2, with $a_1$=$S_1$). This recovers the general term from the partial sum formula. The method of differences also helps identify the general term of sequences like 2,5,10,17,26,...: differences are 3,5,7,9,...(AP with d=2), so $a_n$ is quadratic. Using three values: $a_n$=$n^{2+1}$.