号码模式

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Coach Gerald enjoys coaching soccer. This year, his team has earned a spot in a regional tournament. The tournament is a knock out tournament. The losing team is automatically out of the tournament and the winning team continues to the next round. Coach Gerald asks his students how many rounds they would have to win in order to be the last team standing. His team was not sure, so he decided to help them by providing part of the pattern that the winners of each round experience.
::杰拉尔德教练喜欢踢足球。今年,他的球队赢得了一场区域锦标赛的一席之地。锦标赛是一场决赛。输球队自动退出锦标赛,获胜队继续下一轮比赛。杰拉尔德教练问学生要赢多少回合才能成为最后一支球队。他的球队不确定,所以他决定通过提供每一场比赛的赢家的模式的一部分来帮助他们。

32, 16, 8, 4, ______

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What is the next number in the pattern that Coach Gerald wrote for his players?
::杰拉尔德教练为他的球员写的图案的下一个数字是什么?

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In this concept, you will learn how to use patterns to solve problems.

::在这个概念中,你将学会如何使用模式解决问题。

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Using Patterns to Solve Problems
::使用模式解决问题

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When solving problems that involve greatest common factors, you can use patterns to help. 
::在解决涉及最大共同因素的问题时,您可以使用模式来提供帮助。

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Let's look at an example.
::让我们举个例子。

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Name the next value in the series. 4, 7, 10, 13, ______
::列出序列中的下一个值 。 4, 7, 10, 13, __

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First, you need to identify the pattern by looking at the numbers.
::首先,你需要通过查看数字来识别模式。

4 + 3 = 7; 7 + 3 =10, 10 + 3 = 13

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The pattern consists of adding 3 to the previous number, so the next number will be the sum of 13 and 3.
::该模式包括上一个数字增加3个,因此下一个数字将是13和3的总和。

13 + 3 = 16

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The answer is 16.
::答案是16岁

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Although the first example involved addition, any of the four operations can be used when trying to identify the pattern. 
::虽然第一个例子涉及增加,但四个业务中的任何一项都可用于确定模式。

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Let's look at an example of a pattern that uses multiplication.
::让我们看看一个使用乘法的模式的例子。

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Name the next value in the series. 2, 6, 18, 54, _____
::列出序列中的下一个值。 2, 6, 18, 54, __

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Notice that the next number is found by multiplying the current number by 3. Based on that pattern, the next number will be the product of 54 and 3.
::请注意,下一个数字是通过将当前数字乘以3而发现的。 根据该模式,下一个数字将是54和3的产物。

  $\begin{array}{r}54\times 3=162\end{array}$

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The next number in the series is 162.
::下一个系列的号码是162。

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Examples
::实例

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Example 1
::例1

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Earlier, you were given a problem about Coach Gerald.
::早些时候,有人给了你一个杰拉尔德教练的问题

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His team is in a tournament in which teams are knocked out in each round. He wants his team to understand the number of games that they will have to win in order to win the tournament, so he provides his team with part of the pattern that the winners of each round experience.
::他的球队在比赛中每场球队都会被击倒。他希望他的球队能了解他们赢得比赛得分的比赛数量,因此他为球队提供每一场比赛的获胜者所遵循的模式的一部分。

32, 16, 8, 4, ______

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What is the next number in the pattern that Coach Gerald wrote for his players?
::杰拉尔德教练为他的球员写的图案的下一个数字是什么?

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First, figure out what changes between the given values.
::首先,找出给定值之间的变化。

32 - 16 = 16; 16 - 8 = 8; 8 - 4 = 4

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Next, look at the changes and determine the pattern. 
::接下来,看看这些变化,确定模式。

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Subtract half of the previous number from the current number to calculate the next number.
::从当前数字中减去上一个数字的一半,以计算下一个数字。

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Then, find the next number.
::然后,找到下一个号码。

4 - 2 = 2

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The answer is 2.
::答案是2。

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Example 2
::例2

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What is the next number in this sequence?
::这个序列的下一个数字是什么?

1, 1, 2, 3, 5, 8, 13, 21, _____

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First, figure out what changes between the given values.
::首先,找出给定值之间的变化。

1 + 0 = 1; 1 + 1 = 2; 2 + 1 = 3; 3 + 2 = 5; 5 + 3 = 8; 8 + 5 = 13; 13 + 8 = 21

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Next, look at the changes and determine the pattern.
::接下来,看看这些变化,确定模式。

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The next number is found by finding the sum of the current number and the number before it.
::下一个号码是通过找到当前号码和现有数字的总和而找到的。

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Then, determine the next number.
::然后,确定下一个数字。

21 + 13 = 34

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The next number is 34.
::下一个号码是34。

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Example 3
::例3

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Name the next value in the series.
::命名序列中的下一个值 。

3, 7, 15, 31, _____

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First, figure out what changes between the given values.
::首先,找出给定值之间的变化。

3 + 4 = 7; 7 + 8 = 15; 15 + 16 = 31

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Next, look at the changes and determine the pattern.
::接下来,看看这些变化,确定模式。

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Add 2 times the previous number that was added
::添加上一个加号的2倍于上一个加号

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Then, determine the next number.
::然后,确定下一个数字。

31 + 2(16) = 31 + 32 = 63

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The answer is 63.
::答案是63。

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Example 4
::例4

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Name the next value in the series.
::命名序列中的下一个值 。

12, 8, 4, _____

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First, figure out what changes between the given values.
::首先,找出给定值之间的变化。

12 - 4 = 8; 8 - 4 = 4  

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Next, look at the changes and determine the pattern.
::接下来,看看这些变化,确定模式。

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Subtract 4 to calculate the next number
::减号 4 以计算下一个数字

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Then, determine the next number.
::然后,确定下一个数字。

4 - 4 = 0

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The answer is 0.
::答案是 0 。

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Example 5
::例5

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Name the next value in the series.
::命名序列中的下一个值 。

2.5, 5, 10, 20, 40, _____

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First, figure out what changes between the given values.
::首先,找出给定值之间的变化。

2.5 + 2.5 = 5; 5 + 5 = 10; 10 + 10 = 20; 20 + 20 = 40 

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Next, look at the changes and determine the pattern.
::接下来,看看这些变化,确定模式。

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Add the current number to itself to calculate the next number
::将当前数字添加到自身以计算下一个数字

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Then, determine the next number.
::然后,确定下一个数字。

40 + 40 = 80

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The answer is 80.
::答案是80

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Review
::回顾

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Figure out the pattern in each of the following problems. Then write in the next number in each pattern.
::找出以下每个问题的模式。 然后在每个模式下写下一个数字 。

1. 2, 4, 6, 8, 10 ____
2. 20, 17, 14, 11, ____
3. 4, 8, 16, 32, ____
4. 200, 100, 50 ____
5. 120, 60, 30, 15, ____
6. 22, 33, 44, 55, 66, ____
7. 4, 12, 36, _____
8. 5, 10, 6, 12, 8, 15, 11, _____
9. 6, 4, 8, 5, 10, 6, 12, _____
10. 5, 11, 6, 13, 7, 15, 8, _____
11. 6, 12, 18, 24, 30, 36, _____
12. 100, 75, 100, 75, 50, 75, _____
13. 200, 50, 12.5, _____
14. 621, 207, 69, _____

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Review (Answers) 
::回顾(答复)

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Click   to see the answer key or go to the Table of Contents and click on the Answer Key under the 'Other Versions' option.
::单击可查看答题键, 或转到目录中, 单击“ 其他版本” 选项下的答题键 。

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Resources
::资源