Title:

3? 4? 7? 12? 19? ( )

Analysis:

The difference between 3 and 4 is 1, that between 4 and 7 is 3, that between 7 and 12 is 5, and that between 12 and 19 is 7.

First, the difference is 1+2=3, 3+2=5, 5+2=7, and every two differences are different. From this, it is inferred that 7+2=9, that is, the next difference is 9.

Because 3+ 1=4, 4+3=7, 7+5= 12, 12+7= 19, the former number is added with the difference to get the latter number, so19+9 =

Looking for the meaning of fill-in-the-blank rules

In fact, it is to strengthen your understanding of the general law of series. Although it has many solutions, it is mainly to cultivate 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.