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.