Sequences and Series

Board: CBSE Class: 11

Chapter Overview

Arithmetic Progression (AP) has constant difference d. Geometric Progression (GP) has constant ratio r. The chapter covers nth term and sum formulas for AP and GP. Sum to infinity exists for GP with |r| < 1.

Arithmetic mean, geometric mean, and the AM-GM inequality are introduced. Special series include sums of natural numbers, squares, and cubes.

Topics Covered

Arithmetic Progression
Sum of AP
Geometric Progression
Sum of GP
Sum to Infinity
Arithmetic Mean
Geometric Mean
AM-GM Inequality
Special Series

Key Formulas

AP: an = a + (n-1)d

AP sum: Sn = n/2(2a + (n-1)d)

GP: an = ar^n-1

GP sum: Sn = a(rⁿ - 1)/(r-1)

GP to inf: S = a/(1-r) for |r| < 1

Real-World Applications

Applications: Population growth (GP), loan amortization (AP/GP), radioactive decay, musical harmony.

Study Tips

Tip: Identify whether a sequence is AP or GP

Tip: Learn all sum formulas by heart

Tip: Understand the AM-GM relationship