The analysis process is as follows:

The first one is over four years old. Remove.

The square of the first number 1 = 1.

The second number 4 = the square of 2.

The third number 9 = the square of 3.

The fourth number = the square of 4.

By analogy, the fifth number =5 squared =25, and the seventh number =7 squared =49.

Extended data:

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 mainly cultivates your ability to discover the general law of series and guess the general term of series (that is, the ability to use incomplete induction).

So that when we encounter some series whose general terms are difficult to find by general methods, we can quickly and accurately guess the general term formula of this series through the first few terms, and then prove it by mathematical induction or reduction to absurdity or other methods, bypassing the main mountain and quickly getting its general term formula. Therefore, finding the rules to fill in the blanks will still help us to enhance our understanding of some difficulties and characteristic series.

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.