1. Let's start with Arithmetic Sequence (AS). An arithmetic sequence is a list of numbers where each term after the first is found by adding a constant difference, called the common difference $d$, to the previous term. 2. The formula for the $n$th term of an arithmetic sequence is: $$a_n = a_1 + (n-1)d$$ where $a_1$ is the first term. 3. The sum of the first $n$ terms (Arithmetic Series, GS) is given by: $$S_n = \frac{n}{2} (2a_1 + (n-1)d)$$ This formula helps find the total of the sequence up to $n$ terms. 4. The index in sequences usually refers to the position $n$ of a term in the sequence. 5. To change the subject of a formula means to rearrange it to make a different variable the subject. For example, from $a = bc$ to $b = \frac{a}{c}$. 6. Factorization is breaking down an expression into simpler factors that multiply to give the original expression. For example, $x^2 - 9 = (x-3)(x+3)$. 7. Percentages represent parts per hundred. To find a percentage of a number, multiply the number by the percentage divided by 100. For example, 20% of 50 is $50 \times \frac{20}{100} = 10$. These are the basics you need to understand these topics clearly.