Answer:

The content of this part of the extended information mainly examines the knowledge points of finding fill-in-the-blank rules:

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.

1, 2, 4, 7, 1 1, 16, (22), (29),-The difference is: 1, 2, 3, 4, 5, 6, …

2,5, 10,17,26, (37), (50)-the difference is: 3,5,7,9, …

0, 3, 8, 15, 24, (35), (48)-the difference is: 3, 5, 7, 9, …

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.