9. Sequences And Series

SEQUENCES AND SERIES CLASS 11 MATHS

By a sequence, we mean an arrangement of number in definite order according to some rule. Also, we define a sequence as a function whose domain is the set of natural numbers or some subsets of the type {1, 2, 3, ….k}. A sequence containing a finite number of terms is called a finite sequence. A sequence is called infinite if it is not a finite sequence.

Let a1, a2, a3, … be the sequence, then the sum expressed as a1 + a2 + a3 + … is called series. A series is called finite series if it has got finite number of terms.

An arithmetic progression (A.P.) is a sequence in which terms increase or decrease regularly by the same constant. This constant is called common difference of the A.P. Usually, we denote the first term of A.P. by a, the common difference by d and the last term by l. The general term or the nth term of the A.P. is given by

an= a + (n – 1) d.

The sum Sn of the first n terms of an A.P. is given by
S_n= \frac{n}{2}(2a + (n - 1) d)

The arithmetic mean A of any two numbers a and b is given by \frac{a + b}{2} i.e., the sequence a, A, b is in A.P.

A sequence is said to be a geometric progression or G.P., if the ratio of any term to its preceding term is same throughout. This constant factor is called the common ratio. Usually, we denote the first term of a G.P. by a and its common ratio by r. The general or the nth term of G.P. is given by an= arn – 1 The sum Sn of the first n terms of G.P. is given by S_n= \frac{a(r^n - 1)}{(r - 1)} = \frac{a(1 - r^n)}{(1 - r)}, {\rm if }   r \ne 1 .

The geometric mean (G.M.) of any two positive numbers a and b is given by \sqrt{ab} i.e., the sequence a, G, b is G.P.

Sequences and Series Lecture 1

Lecture - 1

Meaning of Sequences Meaning of General Term (nth term) Meaning of Series NCERT Exercise 9.1 (Q1 to Q14)  Fibonacci Sequence
Sequences and Series Lecture 2

Lecture - 2

Meaning and Basics of Arithmetic Progression Derivation for nth term (General term) of Arithmetic Progression Derivation for Sum to n terms of a Arithmetic Progression Relationship between Arithmetic Progression and Arithmetic Mean NCERT Exercise 9.2 (Q1 to Q4)