Find a formal introduction:

Discovery mode is a basic skill in mathematics teaching in primary and secondary schools. The purpose is to let students discover, experience and explore the simple arrangement rules of figures and numbers. Through comparison, we can understand and master the method of discovering patterns, and cultivate students' preliminary observation, operation and reasoning ability. Fill in the blanks with rules, and let students find the simple arrangement rules of figures and numbers through observation, experiment, guessing and reasoning.

The significance of finding the law to fill in the blanks is actually to strengthen the understanding of the general law of sequence. Although it has many solutions, it is mainly to cultivate your ability to find the general law of series and guess the general term of series (that is, the ability to use incomplete induction), so that when you encounter some series that are difficult to find the general term by general methods,

We can guess the general formula of this series quickly and accurately through the first few items, and then prove it by mathematical induction or reduction to absurdity or other methods, bypassing the front mountain and quickly getting its general formula. Therefore, finding the rules to fill in the blanks will still help us to enhance our understanding of some difficulties and characteristic series.

Find a pattern to fill in the blanks: 9- 1 = 8, 16-4 = 12, 25-9 = 16, 36- 16 = 20, 49-25 = 24. There are countless patterns. Some given numbers are regular, and some are regular between every other number. The difference between two adjacent numbers also has certain regularity. The law may be the same addition, the same subtraction, the multiplication of the same number or series, or the square.

Scope of application:

Finding the method in primary school is very simple. Only addition, subtraction, multiplication and division will not have the troublesome solution of square, although sometimes addition, subtraction, multiplication and division will have square.

Middle school is a little more difficult. If you add power to the square, you may use arithmetic progression to find the law. But if you study hard, it's still very simple. There is basically no problem in finding patterns in universities. There may be, but the chances are slim, so don't worry.