1. Let's start with the basics of Arithmetic Sequences (AS) and Geometric Sequences (GS). 2. An Arithmetic Sequence is a sequence where each term increases by a constant difference $d$. The $n$th term is given by the formula: $$a_n = a_1 + (n-1)d$$ where $a_1$ is the first term. 3. The sum of the first $n$ terms of an Arithmetic Sequence (Arithmetic Series) is: $$S_n = \frac{n}{2} (2a_1 + (n-1)d)$$ 4. A Geometric Sequence is a sequence where each term is multiplied by a constant ratio $r$. The $n$th term is: $$a_n = a_1 r^{n-1}$$ 5. The sum of the first $n$ terms of a Geometric Sequence (Geometric Series) is: $$S_n = a_1 \frac{1-r^n}{1-r} \quad \text{for } r \neq 1$$ 6. To change the subject of a formula, isolate the variable you want on one side using algebraic operations like addition, subtraction, multiplication, division, and factoring. 7. Factorization involves expressing an expression as a product of its factors. For example, $x^2 - 9 = (x-3)(x+3)$. 8. Percentage problems often involve finding a part of a whole or the whole from a part using the formula: $$\text{Percentage} = \frac{\text{Part}}{\text{Whole}} \times 100$$ 9. Practice example: Find the sum of the first 10 terms of an arithmetic sequence where $a_1=3$ and $d=2$. 10. Using the sum formula: $$S_{10} = \frac{10}{2} (2 \times 3 + (10-1) \times 2) = 5 (6 + 18) = 5 \times 24 = 120$$ 11. Practice example: Find the sum of the first 5 terms of a geometric sequence where $a_1=2$ and $r=3$. 12. Using the sum formula: $$S_5 = 2 \frac{1-3^5}{1-3} = 2 \frac{1-243}{1-3} = 2 \frac{-242}{-2} = 2 \times 121 = 242$$ This covers the key concepts and formulas for your revision.