Observing the law of sequence, we can find that the difference between each number and the previous number is increasing. The difference between 1 and 2 is 1, 2 to 4 is 2, 4 to 7 is 3, 7 to 1 1 is 4. According to this rule, we can infer that the next number should be 1 1 plus the difference of 4, that is, 16.
By testing the law, we bring 16 into the last number of the sequence 1 1, and then calculate the difference of 4 to get 16. So 16 is the next number that conforms to the law of sequence.
Sequence problem is a common problem in mathematics. To solve the problem of series, we need to observe the law between numbers, find out the recursive relationship of series, and then infer the next number. This reasoning and analysis ability is very important in mathematics and logical thinking, which can cultivate our abstract thinking and problem-solving ability.
First of all, obey the law of order
Observing a given sequence, we can find that there are different addition rules between each number and the previous number.
Second, the legal analysis
The difference between 1 and 2 is 1, the difference between 2 and 4 is 2, the difference between 4 and 7 is 3, and the difference between 7 and 1 1 is 4. It is not difficult to find that the law is increasing in turn. According to this rule, the next number should be 1 1 plus the difference of 4, which is 16.
Third, the inspection method
We can compare 16 with the given sequence to see if it conforms to the law. Starting from 1 1, add the difference by 4 in turn, and you can get 16, which conforms to the law.
Sequence and sequence law
A sequence is an ordered series of numbers. By observing and analyzing the law between numbers in a series, we can find out the law or formula of the series, so as to predict or calculate other numbers in the series.
The common laws of series are arithmetic progression and geometric progression. Arithmetic progression means that the difference between adjacent elements in an exponential column is a fixed number, while geometric progression means that the ratio of adjacent elements in an exponential column is a fixed number.
When solving the problem of sequence, we can find out the law between different numbers by observing the relationship between numbers in sequence, so as to get the general formula or recursive relationship of sequence. By calculating or using the known series formula, the number at any position in the series can be obtained.