SEQUENCE AND SERIES

GO TO SEQUENCE AND SERIES

SEQUENCE AND SERIES

SEQUENCE – An arrangement of numbers in a definite order according to some rules.

TERM – various numbers occurring in a sequence are called its terms.  

We denote a sequence as :

        a₁, a₂, a₃, …, a_n

It is a sequence having n terms. a₁ is the first term and a_n is the n^th term. n^th term is also called the general term of a sequence.

Sequence having finite number of terms is called finite sequence and sequence having infinite number of terms is called infinite sequence.

1.      Arithmetic Progression (A.P)

        A sequence   a₁, a₂, a₃, …, a_n is called arithmetic progression if a_n+1 = a_n + d, n ϵ N

       2.      Geometric Progression (G.P.) 

A sequence   a₁,a₂,a₃,…,a_n is called geometric progression if each term is non-zero and, a_k+1/ a_k =r (constant) for all k ≥ 1

        a, ar, ar², ar³,… is a G.P. where a is the first term and r is the common ratio.