Today, in our math club, the teacher gave us an interesting topic, which is actually a somewhat complicated topic to find the law. The title is like this: "There is a column number: 1, 2, 3, 2, 1, 2, 3, 4, 3, 2, 3, 4, 5, 4, 3. What is the sum of the top 240 numbers in this column? " As soon as I got the topic, it suddenly occurred to me that this topic must be done according to law.

Idea 1: First, I will try to sum in groups of three, 6, 5, 10, 9, 12, 15, 14. In this way, these figures have their own characteristics, and the key is that they can't find a suitable law. So, I found a group of four to sum, 8, 10, 12,16,20. After a careful look, it seems that there is no rule, so I have to try to find a group of five to sum, 9, 14, 19, 24 ..., so obviously they are equal series, I am very happy, and then 240÷5=48 (group), a group of five, (6544. (4, 5, 6, 5, 4) ... Then we can find the sum of the last term, 9+47×5=244, and divide the sum of the first term and the last term by 2, (9+244)×48÷2=6072. That's it!

Idea 2: I also found that the first number at the beginning of each group is exactly 1, 2, 3, 4...48, so I came up with another method, (1+48) × 48× 2+(2+49 )× 48× 2. It is reasonable to think so, and it is also a clear and practical method!

Idea 3: I also find that when there are n groups, his sum is also the sum of (1+2+3+4+n) × 5+4n = the number of n groups you need, for example, (1+2+3+4+...+48. Although this rule is somewhat abstract, it is simpler than the other two methods if you understand it yourself.

All I did was three of them. In fact, there are many ways, but I have to find the rules myself and solve the mystery myself!