Type 1: Find the sum of n terms Identify general term $t_k$. Decompose into standard summable parts. Apply sum formulas.

Type 2: Find the nth term given $S_n$ Use $a_n$ = $S_n$ - $S_{n-1}$ for n >= 2. Check $a_1$ = $S_1$ separately.

Type 3: Three/four terms in AP or GP Assume symmetric forms: AP -> a-d, a, a+d. GP -> a/r, a, ar. Use given conditions to find a and d (or r).

Type 4: Prove three quantities are in AP/GP/HP For AP: show 2b = a+c. For GP: show $b^2$ = ac. For HP: show 1/a, 1/b, 1/c are in AP.

Type 5: AGP summation Identify AP and GP parts. Apply S - rS technique.

Type 6: Telescoping series Use partial fractions to decompose $\frac{1}{f(k}$*g(k)). Most terms cancel.

Type 7: AM-GM optimization Use AM >= GM to find minimum of sums or maximum of products under constraints.

Time allocation: Standard AP/GP problems: 1-2 minutes. Series with decomposition: 2-3 minutes. AGP or telescoping: 3-4 minutes.