11th Class Mathematics Sequence and Series Introduction

      Introduction

The ordered collection of objects is called sequence. The sequence having specified patterns is called progression. In this chapter besides discussing about the arithmetic progression, we will also discuss about the geometric progression and arithmetic-geometric progression. The various numbers occurring in the sequence is called term of the sequence. A sequence having finite number of terms is called finite sequence, where as the sequence having infinite number of terms is called infinite sequence.

The real sequence is that sequence whose range is a subset of the real number.

A series is defined as the expression denoting the sum of the terms of the sequence. The sum is obtained after adding the terms of the sequence. If \[{{a}_{1}},{{a}_{2}},{{a}_{3}},---,{{a}_{n}}\] is a sequence having n terms, then the sum of the series is given by,

\[\sum\limits_{n=1}^{m}{{{a}_{n}}={{a}_{1}}+{{a}_{2}}+{{a}_{3}}+----{{a}_{n}}}\]