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Summary Number Patterns and Sequences

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This summary includes the equations used for the following types of patterns and the steps that can be used to obtain each equation from the pattern given: 1. Linear Patterns 2. Quadratic Patterns 3. Exponential Patterns 4. Arithmetic Sequences 5. Gemoetric Sequences

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Institution
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November 10, 2021
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Written in
2020/2021
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𝑻𝒏 = 𝒂𝒏 + 𝒄
Linear Patterns 𝒚 = 𝒎𝒙 + 𝒄

𝑻𝒏 = 𝒂𝒏𝟐 + 𝒃𝒏 + 𝒄
Quadratic Patterns 𝒚 = 𝒂𝒙𝟐 + 𝒃𝒙 + 𝒄

𝑻𝒏 = 𝒂𝒃𝒏
Exponential Patterns 𝒚 = 𝒂𝒃𝒙


Arithmetic Sequences 𝑻𝒏 = 𝒂 + 𝒏 − 𝟏 𝒅


Geometric Sequences 𝑻𝒏 = 𝒂𝒓𝒏−𝟏

, Linear Patterns
𝑻𝒏 = 𝒂𝒏 + 𝒄
𝒚 = 𝒎𝒙 + 𝒄
𝑷𝒂𝒕𝒕𝒆𝒓𝒏: 𝑇1 ; 𝑇2 ; 𝑇3 ; 𝑇4 …

𝑇1 𝑇2 𝑇3 𝑇4
Step 1:
Substitute a (numerical difference
into 𝑻𝒏 = 𝒂𝒏 + 𝒄
𝑇3 − 𝑇2 𝑇4 − 𝑇3
𝑇2 − 𝑇1

1st Difference is constant
Step 2:
Substitute (𝒏; 𝑻𝒏 ) (data pair) into
∴ 𝑇2 − 𝑇1 = 𝑇3 − 𝑇2 = 𝑇4 − 𝑇3 = a 𝑻𝒏 = 𝒂𝒏 + 𝒄

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