When to use: When the differences of consecutive terms form an AP or GP.

Technique:

1. Compute first differences: d_k = a_{k+1} - a_k
2. If d_k is constant: original sequence is AP
3. If d_k forms an AP: second differences are constant, so a_n is quadratic in n
4. If d_k forms a GP: sum the GP to find a_n

Example: Sequence 2, 5, 10, 17, 26, ... Differences: 3, 5, 7, 9, ... (AP with d=2) Second differences: 2, 2, 2, ... (constant) So a_n = An^2 + Bn + C. Using a_1=2, a_2=5, a_3=10: A+B+C=2, 4A+2B+C=5, 9A+3B+C=10. Solving: A=1, B=0, C=1. So a_n = n^2 + 1.