## Arithmetic and Geometric Progressions

Tags: #math #arithmetic #geometric #progressions### Equation

$$S_{n}=a+(a+d)+(a+2d)+...+[a+(n-1)d]=\frac{n}{2}[2a+(n-1)d] \\ S_{n}=a+ar+ar^{2}+...+ar^{n-1}=a\frac{1-r^{n}}{1-r}$$### Latex Code

S_{n}=a+(a+d)+(a+2d)+...+[a+(n-1)d]=\frac{n}{2}[2a+(n-1)d] \\ S_{n}=a+ar+ar^{2}+...+ar^{n-1}=a\frac{1-r^{n}}{1-r}

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### Introduction

#### Explanation

- Arithmetic progressions: Arithmetic progressions is calculated as . The first number is a, and the consecutive series number follows the pattern of at the number at the (n-1) th position is .
- Geometric progressions: Geometric progressions is calculated as . The first number is a, and the consecutive series number follows the pattern of with multiplier as r and at the the number at (n-1) th position is .

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