The observation rule should be 1 white beads 1 black beads 2 white beads 1 black beads 3 white beads 1 black beads 4 white beads 1 black beads 5 white beads 1 black beads 6 white beads 1 black beads. According to this rule, the box should be covered with 4 white beads 1 black beads, 5 white beads, ***9 white beads 1 black beads.

Four common ways to solve standard questions are as follows:

First, mark the serial number. We put the known numbers and the corresponding serial numbers together to observe and compare, and the common one is arithmetic progression.

Second, the common factor method. Divide the given number by the least common factor and multiply it to see if it is related to n or 2n, 3n.

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Third, the first digit method. A given number is subtracted, added, multiplied or divided with the first digit at the same time to form a new series, and then the relationship with the serial number can be found, and the law can be found.

4. Separate odd numbers from even numbers. List the odd-numbered digits and even-numbered digits respectively to form two series, and then find out the rules.

This kind of question can also be used to 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: a 1+(n- 1)b, where a is the first digit of the sequence and b is the increment, (n- 1). Then simplify the algebraic expression a+(n-1) b.

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For example: 4, 10, 16, 22, 28 ... Find the nth number. Analysis: Starting from the second bit, each bit is 6 more than the previous bit, and the increase rate is 6, so the nth bit is: 4+(n- 1)6=6n-2.

2, if the increase is not equal, but the increase is the same (that is, the increase is equal, that is, the increase is 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. The basic idea is: find the increment from n- 1 to n, and find the total increment from 1 to n. 1 This number plus the total increment is the nth digit.

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3. The growth rates are not equal, but increase year-on-year, that is, the growth rates are in geometric series, such as 2, 3, 5, 9, 17, and the growth rates are 1, 2, 4 and 8.

4, increase is not equal to, increase is not equal to (that is, increase is not equal to). There is probably no general solution to this kind of problem, but only analytical observation, but this kind of problem includes the second kind of problem, such as using analytical observation, and there are some skills.