Sequences & Series contributes 2-3 questions annually in JEE Main, testing algebraic manipulation and pattern recognition. The chapter covers four main progression types and special summation techniques.

Arithmetic Progression (AP) has constant difference d with nth term a+(n-1)d and sum n/2*(2a+(n-1)d). Geometric Progression (GP) has constant ratio r with nth term ar^(n-1) and sum a$\frac{r^n-1}{(r-1)}$. Infinite GP converges to $\frac{a}{1-r}$ when |r|<1. Harmonic Progression (HP) is defined as the reciprocal of an AP with no direct sum formula.

Special series formulas are critical: sum(k)=n$\frac{n+1}{2}$, sum($k^2$)=n(n+1)$\frac{2n+1}{6}$, sum($k^3$)=[n$\frac{n+1}{2}$]^2. The identity sum($k^3$)=[sum(k)]^2 is frequently tested.

The AGP technique (S-rS) handles series where terms are products of AP and GP terms. Telescoping series use partial fractions to decompose terms into canceling differences. The AM-GM-HM inequality (AM>=GM>=HM for positive reals) is used for optimization.

Key problem types: finding terms from conditions, summing series with general terms, proving AP/GP/HP relationships, AGP summation, and AM-GM optimization. The most common trap is using n instead of (n-1) in nth term formulas.