The basic method-look at the increase

1. If the increase is equal (actually arithmetic progression): compare each number with its previous one. If the increments are equal, the nth number can be expressed as: an (n-L) b, where a is the first digit of the sequence, b is the increment, and (n- 1) b is the total increment from the first digit to the nth digit. Then simplify the algebraic expression a (n-1) b.

For example: 4, 10, 16, 22, 28 ... Find the nth number.

Analysis: Starting from the second digit, the number of digits is 6 more than the previous digit, with an increase rate of 6. So the nth digit is: 4(n- 1) 6 = 6n-2.

2, the proportion is equal (geometric series):

For example: 2, 4, 8, 16, ... the nth item is: an=2 "

3. If the growth rates are not equal, but the growth rates increase by the same amount (that is, the growth rates are equal, that is, the secondary arithmetic progression). If the growth rates are 3, 5, 7 and 9 respectively, it means that the growth rate has increased by the same amount. The number of the nth bit of this series also has a general solution.

4. the growth rate is not equal, but year-on-year, that is, the growth rate is geometric series.

Such as: 2, 3, 5, 9, 17, ...

Analysis: Sequence 2, 3, 5, 9, 17. The growth rate is 1, 2, 4, 8 ... that is, the growth rate is a geometric series with a ratio of 2.