Concept of Sequences



  • Sets and Relations
  • Functions
  • Complex Numbers 33
  • Sequences and Series
    • Concept of Sequences
    • Geometric Progression (G.P.)
    • General Term Or the nth Term of a G.P.
    • Sum of the First n Terms of a G.P.
    • Sum of Infinite Terms of a G. P.
    • Recurring Decimals
    • Harmonic Progression (H. P.)
    • Types of Means
    • Special Series (Sigma Notation)
  • Locus and Straight Line
    • Locus
    • Equation of Locus
    • Line
    • Equations of Lines in Different Forms
    • General Form Of Equation Of Line
  • Determinants
    • Determinants
    • Properties of Determinants
    • Application of Determinants
    • Cramer’s Rule
    • Consistency of Three Linear Equations in Two Variables
    • Area of a Triangle Using Determinants
    • Collinearity of Three Points
  • Limits
    • Definition of Limit of a Function
    • Algebra of Limits
    • Evaluation of Limits
    • Direct Method
    • Factorization Method
    • Rationalization Method
    • Limits of Exponential and Logarithmic Functions
  • Continuity
    • Continuous and Discontinuous Functions
    • Continuity of a Function at a Point
    • Definition of Continuity
    • Continuity from the Right and from the Left
    • Properties of Continuous Functions
    • Continuity in the Domain of the Function
    • Examples of Continuous Functions Whereever They Are Defined
  • Differentiation
    • The Meaning of Rate of Change
    • Definition of Derivative and Differentiability
    • Derivative by the Method of First Principle
    • Rules of Differentiation (Without Proof)
    • Applications of Derivatives
  • Partition Values
    • Concept of Median
    • Partition Values
    • Quartiles
    • Deciles
    • Percentiles
    • Relations Among Quartiles, Deciles and Percentiles
    • Graphical Location of Partition Values
  • Measures of Dispersion
    • Measures of Dispersion
    • Range of Data
    • Quartile Deviation (Semi - Inter Quartile Range)
    • Variance and Standard Deviation
    • Standard Deviation for Combined Data
    • Coefficient of Variation
  • Skewness
    • Skewness
    • Asymmetric Distribution (Positive Skewness)
    • Asymmetric (Negative Skewness)
    • Measures of Skewness
    • Karl Pearson’S Coefficient of Skewness (Pearsonian Coefficient of Skewness)
    • Features of Pearsonian Coefficient
    • Bowley’s Coefficient of Skewness
  • Bivariate Frequency Distribution and Chi Square Statistic
    • Bivariate Frequency Distribution
    • Classification and Tabulation of Bivariate Data
    • Marginal Frequency Distributions
    • Conditional Frequency Distributions
    • Categorical Variables
    • Contingency Table
    • Chi-Square Statistic ( χ2 )
  • Correlation
    • Correlation
    • Concept of Covariance
    • Properties of Covariance
    • Concept of Correlation Coefficient
    • Scatter Diagram
    • Interpretation of Value of Correlation Coefficient
  • Permutations and Combinations
    • Introduction of Permutations and Combinations
    • Fundamental Principles of Counting
    • Concept of Addition Principle
    • Concept of Multiplication Principle
    • Concept of Factorial Function
    • Permutations
    • Permutations When All Objects Are Distinct
    • Permutations When Repetitions Are Allowed
    • Permutations When All Objects Are Not Distinct
    • Circular Permutations
    • Properties of Permutations
    • Combination
    • Properties of Combinations
  • Probability
  • Linear Inequations
  • Commercial Mathematics
    • Percentage
    • Profit and Loss
    • Simple and Compound Interest (Entrance Exam)
    • Depreciation
    • Partnership
    • Goods and Service Tax (GST)
    • Shares and Dividends
  • Finite sequence 
  • Infinite sequence
  • Progression


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`. 

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