4.2.4
Arithmetic Sequences
Arithmetic Sequence
Arithmetic Sequence
Terms in arithmetic sequences change by a constant amount each time.
![Illustrative background for Arithmetic sequence](https://image-v2.cdn.app.senecalearning.com/2019-10/b6f391be-c598-49aa-b50f-4027db5095da/common%20difference,h_400,q_80,w_640.png)
![Illustrative background for Arithmetic sequence ?? "content](https://image-v2.cdn.app.senecalearning.com/2019-10/b6f391be-c598-49aa-b50f-4027db5095da/common%20difference,h_400,q_80,w_640.png)
Arithmetic sequence
Arithmetic sequence
- An arithmetic sequence is a sequence that has the property that the difference between any two consecutive terms is a constant.
- This difference is called the common difference, and is represented by the symbol .
![Illustrative background for Explicit formula](https://image-v2.cdn.app.senecalearning.com/2019-10/c95bab78-e520-48aa-bcba-09e6733fb8d9/nth%20term,h_400,q_80,w_640.png)
![Illustrative background for Explicit formula ?? "content](https://image-v2.cdn.app.senecalearning.com/2019-10/c95bab78-e520-48aa-bcba-09e6733fb8d9/nth%20term,h_400,q_80,w_640.png)
Explicit formula
Explicit formula
- Given the first term and the common difference of an arithmetic sequence, we can find the nth term of the sequence an by using the explicit fomula:
- Where .
![Illustrative background for Recursive formula](https://image-v2.cdn.app.senecalearning.com/2020-01/e00aa746-5c4d-4848-ab2e-28185802a454/arithmetic-recursive-formula,h_400,q_80,w_640.png)
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Recursive formula
Recursive formula
- Some arithmetic sequences are defined in terms of the previous term using a recursive formula:
- Where .
1Proof
1.1Types of Numbers
1.2Notation
2Algebra & Functions
2.1Powers & Roots
2.2Quadratic Equations
2.3Inequalities
2.4Polynomials
2.5Graphs
2.7Transformation of Graphs
3Coordinate Geometry
3.1Straight Lines
3.2Circles
3.2.1Equations of Circles centred at Origin
3.2.2Finding the Centre & Radius
3.2.3Equation of a Tangent
3.2.4Circle Theorems - Perpendicular Bisector
3.2.5Circle Theorems - Angle at the Centre
3.2.6Circle Theorems - Angle at a Semi-Circle
3.2.7Equation of a Perpendicular Bisector
3.2.8Equation of a Circumcircle
3.2.9Circumcircle of a Right-angled Triangle
3.3Parametric Equations (A2 only)
4Sequences & Series
4.1Binomial Expansion
5Trigonometry
5.2Trigonometric Functions
5.3Triangle Rules
6Exponentials & Logarithms
6.1Exponentials & Logarithms
7Differentiation
7.1Derivatives
7.2Graphs & Differentiation
7.3Differentiation With Trigonometry and Exponentials
7.4Rules of Differetiation (A2 only)
7.5Parametric & Implicit Differentiation
8Integration
8.1Integration
9Numerical Methods
9.1Finding Solutions
9.2Finding the Area
10Vectors
10.12D Vectors
10.23D Vectors
10.3Vector Proofs
Jump to other topics
1Proof
1.1Types of Numbers
1.2Notation
2Algebra & Functions
2.1Powers & Roots
2.2Quadratic Equations
2.3Inequalities
2.4Polynomials
2.5Graphs
2.7Transformation of Graphs
3Coordinate Geometry
3.1Straight Lines
3.2Circles
3.2.1Equations of Circles centred at Origin
3.2.2Finding the Centre & Radius
3.2.3Equation of a Tangent
3.2.4Circle Theorems - Perpendicular Bisector
3.2.5Circle Theorems - Angle at the Centre
3.2.6Circle Theorems - Angle at a Semi-Circle
3.2.7Equation of a Perpendicular Bisector
3.2.8Equation of a Circumcircle
3.2.9Circumcircle of a Right-angled Triangle
3.3Parametric Equations (A2 only)
4Sequences & Series
4.1Binomial Expansion
5Trigonometry
5.2Trigonometric Functions
5.3Triangle Rules
6Exponentials & Logarithms
6.1Exponentials & Logarithms
7Differentiation
7.1Derivatives
7.2Graphs & Differentiation
7.3Differentiation With Trigonometry and Exponentials
7.4Rules of Differetiation (A2 only)
7.5Parametric & Implicit Differentiation
8Integration
8.1Integration
9Numerical Methods
9.1Finding Solutions
9.2Finding the Area
10Vectors
10.12D Vectors
10.23D Vectors
10.3Vector Proofs
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