1. The problem is to understand what arithmetic and geometric sequences are. 2. An arithmetic sequence is a sequence of numbers where the difference between consecutive terms is constant. This difference is called the common difference $d$. 3. 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 and $d$ is the common difference. 4. A geometric sequence is a sequence where each term is found by multiplying the previous term by a constant called the common ratio $r$. 5. The formula for the $n$-th term of a geometric sequence is: $$a_n = a_1 \times r^{n-1}$$ where $a_1$ is the first term and $r$ is the common ratio. 6. Important rules: - In arithmetic sequences, add or subtract the common difference to get the next term. - In geometric sequences, multiply or divide by the common ratio to get the next term. 7. Example of arithmetic sequence: 2, 5, 8, 11, ... with $d=3$. 8. Example of geometric sequence: 3, 6, 12, 24, ... with $r=2$. This explains the basic concepts and formulas for arithmetic and geometric sequences.