1, arithmetic progression: If the difference between any two adjacent items in a series is constant, that is, the difference between each item and its previous item is equal to the same constant, then this series is called arithmetic progression. For example, the first term is arithmetic progression, 2, 5, 8, 1 1, 14, 17, and the algebraic expression of the nth term is equal to the first term plus n- 1 fixed values.

2. Geometric series: If the ratio of any two adjacent items in a series is constant, that is, the ratio of each item to its previous item is equal to the same constant, then this series is called geometric series. Square series and cubic series are both based on the power operation of numbers.

3. Odd-even series: A series of numbers arranged in a certain order is called a series. Generally, a 1, a2, a3, …, an is used to represent a series, which can be abbreviated as an. The existing series (an) satisfies a relationship: an+ 1=-nan+ 1, (n= 1, 2,3, ..., n), a 1=2. Calculate the values of a2, a3 and a4 according to the known conditions, and then make inductive guesses.

Skills and methods of doing math problems

1. Understand the topic: You need to make sure that you fully understand the requirements of the topic. If you don't understand anything, make these questions clear first. Make a plan. Before you start to solve the problem, you should make a plan to solve the problem. This plan should include how you plan to solve this problem and what mathematical skills or formulas you need to use.

2. Check your work: After you solve the problem, you should take the time to check whether your answer is correct. This may include recalculating your answers, or checking whether your answers meet the requirements of the topic. Practice, mathematics is a subject that needs a lot of practice. Through a lot of practice, you can improve your problem-solving skills and understanding of various mathematical concepts.

3. Use graphics and charts: When solving some complex math problems, using graphics and charts can help you better understand the problems and find solutions. It may take some time to solve math problems patiently, especially those that are more complicated. You need to be patient and don't give up because you can't find the answer at first.

4. Learn and use formulas: There are many formulas in mathematics that can help you solve problems. You should learn and remember these formulas and use them when necessary. Analysis error. If your answer is wrong, you should take the time to analyze why you made the mistake, so that you can avoid making the same mistake in the future.