1. Let's start by understanding what a sequence is: a sequence is an ordered list of numbers following a specific pattern. 2. To formulate an equation for a sequence, we often look for a formula that gives the $n$-th term, denoted as $a_n$, based on its position $n$. 3. There are two common types of sequences: arithmetic and geometric. 4. For an arithmetic sequence, the difference between consecutive terms is constant. The formula is: $$a_n = a_1 + (n-1)d$$ where $a_1$ is the first term and $d$ is the common difference. 5. For a geometric sequence, each term is multiplied by a constant ratio $r$. The formula is: $$a_n = a_1 \times r^{n-1}$$ where $a_1$ is the first term and $r$ is the common ratio. 6. To find the formula for a given sequence, identify if the sequence is arithmetic or geometric by checking the differences or ratios between terms. 7. Once identified, plug in the values of $a_1$ and $d$ or $r$ into the respective formula. 8. For example, if the sequence is 2, 5, 8, 11,... the difference $d$ is 3, so the formula is: $$a_n = 2 + (n-1) \times 3 = 3n - 1$$ 9. If the sequence is 3, 6, 12, 24,... the ratio $r$ is 2, so the formula is: $$a_n = 3 \times 2^{n-1}$$ 10. This approach helps you write equations for many common sequences. Keep practicing with different sequences to get comfortable formulating their equations!