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# The Strategies of Looking for a Pattern and Making an Organized List Practice Questions

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Updated on Oct 3, 2011

To review these concepts, go to The Strategies of Looking for a Pattern and Making an Organized List Study Guide.

## The Strategies of Looking for a Pattern and Making an Organized List Practice Questions

### Practice 1

In each of the questions in the practice that follows, apply the strategy of looking for a pattern to help simplify the problem. Use the answer explanations at the end of the lesson to check your work and your solution.

#### Problems

1. Jake made a pattern by writing the following numbers.
2, 4, 8, 16, 32,_____
2. If he continued the pattern, what would be the next number in this list?

3. A pattern of numbers is as follows: 1, 3, 7, 15, 31, … What would be the eighth number in the pattern?
4. There are four people at a meeting. If each person will shake hands with another person in the room exactly once, how many handshakes will take place at the meeting?
5. A function table is shown next.
6. What is the unknown number in the table?

#### Solutions

1. Read and understand the question. The question is looking for the next number in a pattern.
2. Make a plan. Find the pattern between the given numbers in the list, and apply this rule to the last known value in the list.

Carry out the plan. The values in the list are doubling; each number is equal to the previous number multiplied by 2. To find the next number, multiply 32 by 2 to get 64. The next number in the list is 64.

Check your work. One way to check this solution is to work from the last number to the first by doing the opposite, or inverse operation. Start with 64 and divide by 2 to get the previous term of 32. Then continue this process to be sure all numbers were generated the same way: 32 ÷ 2 = 16; 16 ÷ 2 = 8; 8 ÷ 2 = 4; 4 ÷ 2 = 2, the starting value. This solution is checking.

3. Read and understand the question. This question is looking for the eighth number in the pattern while the first five numbers are given.
4. Make a plan. Find the rule and continue the pattern to the eighth number.

Carry out the plan. Each of the numbers in the list is odd. The difference between the first two numbers is 2, the difference between the second and the third number is 4, the difference between the third and the fourth is 8, and the difference between the fourth and the fifth number is 16. Each time, the difference between the terms doubles so that the sixth term would be 31 + 32 = 63; the seventh would be 63 + 64 = 127; and the eighth term would be 127 + 128 = 255. The eighth term would be 255.

Check your work. Another explanation of the rule is that the difference between two consecutive numbers in the list is always one more than the smaller number. For example, the number following 31 is equal to 31 + (31 +1) = 31 + 32 = 63. This is another way to extend this pattern to eight terms. Thus, the seventh term is 63 + (63 + 1) = 127, and the eighth term is 127 + (127 + 1) = 255.

5. Read and understand the question. This problem is looking for the number of handshakes for a group of people, and each person will shake hands with another exactly one time. It is understood that a person would not shake hands with himself or herself.
6. Make a plan. One approach to this question is to make a table of values. In the first column, list the number of people at the meeting and in the second column, list the number of handshakes that would take place. Start the table with one person, and look for a pattern from there.

Carry out the plan. If there is only one person at the meeting, there will not be any handshakes. If there are two people at the meeting, there will be one handshake. If there are three people, then the first person and second person shake hands, the second and third person shake hands, and the first and third person shake hands. This is a total of 3 handshakes. Examine these values in a table vertically.

As you read down, the number of people increases by 1 each time. In the second column, the number of handshakes increases by adding one more than the previous increase. For example, add 1, then add 2, then add 3, and so on. To complete the table, use this pattern: 0 + 1 = 1, 1 + 2 = 3, so 3 + 3 = 6. There are 6 handshakes among 4 people.

Check your work. In order for each person to shake hands with each other person, person 1 would shake hands with person 2, person 3, and person 4. This is a total of 3 handshakes so far. Person 2 would now have to shake hands with person 3 and person 4, for an additional 2 handshakes. Person 3 would then need to shake hands with person 4 to complete the handshakes. This is a total of 3 + 2 + 1 = 6 handshakes, which is the same conclusion you drew by making the table.

7. Read and understand the question. You are looking for the missing value in a table where most of the numbers are given.
8. Make a plan. Look for a pattern in the table to help you figure out the missing number. This pattern can be a horizontal (across) or vertical (up/down) pattern.

Carry out the plan. In this table, each of the values is filled in except for the location of the question mark, so look for a pattern with the other numbers. For each given x-value, the corresponding y-value is one more than double the x-value. Check each row to make sure the pattern holds true for all numbers in the table. By using this pattern, the missing number is 2 × 5 + 1 = 11.

Check your answer. Another way to view this table is vertically. As the y-values increase, each number is two more than the previous one. By using this method, the missing number is 9 + 2 = 11, which is the same answer you found by the other method.

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