#### Topics

##### Sets and Relations

##### Functions

##### Complex Numbers 33

##### Sequences and Series

##### Locus and Straight Line

##### Determinants

##### Limits

##### Continuity

##### Differentiation

##### Partition Values

##### Measures of Dispersion

##### Skewness

##### Bivariate Frequency Distribution and Chi Square Statistic

##### Correlation

##### Permutations and Combinations

- Introduction of Permutations and Combinations
- Fundamental Principles of Counting
- Concept of Addition Principle
- Concept of Multiplication Principle
- Concept of Factorial Function
- Concept of Permutations
- Permutations When All Objects Are Distinct
- Permutations When Repetitions Are Allowed
- Permutations When All Objects Are Not Distinct
- Circular Permutations
- Properties of Permutations
- Concept of Combinations
- Properties of Combinations

##### Probability

##### Linear Inequations

##### Commercial Mathematics

#### description

- Finite sequence
- Infinite sequence
- Progression

#### notes

Let us consider the following examples: Assume that there is a generation gap of 30 years, we are asked to find the number of ancestors, i.e., parents, grandparents, great grandparents, etc. that a person might have over 300 years.

Here, the total number of generations = `300 /30 =10`

The number of person’s ancestors for the first, second, third, …, tenth generations are 2, 4, 8, 16, 32, …, 1024. These numbers form what we call a sequence.

The `n^(th)` term is the number at the nth position of the sequence tand is denoted by `a^n`.The `n^(th)` term is also called the general term of the sequence.

A sequence containing finite number of terms is called a finite sequence. For example, sequence of ancestors is a finite sequence since it contains 10 terms (a fixed number).

A sequence is called infinite, if it is not a finite sequence. For example, the sequence of successive quotients mentioned above is an infinite sequence, infinite in the sense that it never ends.

a sequence can be regarded as a function whose domain is the set of natural numbers or some subset of it. Sometimes, we use the functional notation a(n) for `a_n`.