This document provides formulas for arithmetic and geometric sequences and series. It gives the formulas to calculate the nth term and sum of terms for an arithmetic sequence, as well as the formula for the sum of terms of an arithmetic series. Similarly, it provides the formulas to calculate the nth term and sum of terms for a geometric sequence, and the formulas for the sum of a finite and infinite geometric series.

1. PRE-CALCULUS 20 – CHAPTER 1 – FORMULA SHEET
ARITHMETIC SEQUENCE: 𝑡 𝑛 = 𝑡1 + ( 𝑛 − 1) 𝑑
ARITHMETIC SERIES: 𝑆 𝑛 =
𝑛
2
[2𝑡1 + ( 𝑛 − 1) 𝑑]
𝑆 𝑛 =
𝑛
2
[ 𝑡1 + 𝑡 𝑛]
GEOMETRIC SEQUENCE: 𝑡 𝑛 = 𝑡1 𝑟 𝑛−1
GEOMETRIC SERIES: 𝑆 𝑛 =
𝑡1 (𝑟 𝑛−1)
𝑟−1
𝑆 𝑛 =
𝑟𝑡 𝑛− 𝑡1
𝑟−1
𝑆∞ =
𝑡1
1−𝑟