Consecutive Integers and Algebra

Consecutive Integers

​As discussed in the introduction, in Maths, the numbers that follow each other in an order are called consecutive numbers or consecutive integers. These integers go from smallest to the highest, i.e. in ascending order. Some of the examples are: -4,-3,-2, −1, 0, 1, 2, 3, 4. 10,11,12,13,14,15,1

Remeber these steps from yesterday?

Click on the link below to watch a Khan Academy video.

https://www.youtube.com/watch?v=8CJ6Qdcoxsc&ab_channel=KhanAcademy

Review this example from yesterday

Multiple Choice

Which of the following setups would be used to find four consecutive integers?

• n

  n+2

  n+4

  n+6

• n

  2n

  4n

  6n

• n+1

  n+2

  n+3

  n+4

• n

  n+1

  n+2

  n+3

Multiple Choice

Find two consecutive integers whose sum is -97.

• -48, 49

• 47, 50

• -49, -50

• -48, -49

Multiple Choice

The sum of three consecutive integers is 48. What are they?

• 16, 17, 18

• 15, 16, 17

• 17, 18, 19

• 24, 25, 26

Multiple Choice

The sum of three consecutive integers is 225. What are the three integers?

• 75, 75, 75

• 100, 75, 75

• 75, 76, 77

• 74, 75, 76

Multiple Choice

The sum of 4 consecutive integers is 182. What are they?

• 61, 62, 63, 64

• 62, 63, 64, 65

• 176, 177, 178, 179

• 44, 45, 46, 47

Multiple Choice

The sum of 5 consecutive integers is -240. What are those integers?

• 46, 47, 48, 49 and 50

• -50, -51, -52, -53 and -54

• -50, -49, -48, -47 and -46

• 50, 51, 52, 53 and 54

Multiple Choice

What two consecutive even integers have a sum of 90?

• 30 and 60

• 43 and 47

• 44 and 46

• 10 and 80

Multiple Choice

Find three consecutive even integers whose sum is 84.

• 26, 28, 30
• 28, 30, 32
• 27, 28, 29
• 24, 26, 28

Multiple Choice

Find three consecutive odd integers whose sum is -45.

• -15, -17, -19

• -17, -18, -19

• -13, -15, -17

Multiple Choice

Find four consecutive odd integers whose sum is 128.

• 32, 34, 37, 38
• 27, 29, 31, 33
• 29, 31, 33, 35
• 25, 27, 29, 31

Consecutive Integers-Algebra

Solve problems relating to Algebra and Consecutive Integers.

Multiple Choice

The sum of three consecutive even integers is 618.  What is the largest number in the group?

• 207
• 209
• 206
• 208

Multiple Choice

Which of the following setups would be used to find four consecutive integers?

• n
  n+2
  n+4
  n+6
• n
  2n
  4n
  6n
• n+1
  n+2
  n+3
  n+4
• n
  n+1
  n+2
  n+3

Multiple Choice

The sum of three consecutive integers is 48.  What is the smallest number in the group?

• 16
• 15
• 17
• 24

Multiple Choice

The sum of three consecutive odd numbers is 597.  What is the smallest number in the group?

• 198
• 199
• 197
• 196

Multiple Choice

The sum of 4 consecutive integers is 180. What is the smallest number in the group?

• 61

• 62

• 176

• 44

Multiple Choice

What two consecutive even integers have a sum of 90?

• 30 and 60
• 43 and 47
• 44 and 46
• 10 and 80 

Multiple Choice

The sum of three consecutive even integers is 618.  What is the largest number in the group?

• 207
• 209
• 206
• 208

Multiple Choice

The sum of 4 consecutive even numbers is 364.  What is the sum of the middle two numbers? 

• 91
• 92
• 183
• 182

Multiple Choice

The sum of three consecutive odd numbers is 597.  What is the smallest number in the group?

• 198
• 199
• 197
• 196

Multiple Choice

Find two consecutive, even integers such that three times the first is eight more than twice the second.

• 12 and 14

• 6 and 8

• 10 and 12

• 8 and 10

Multiple Choice

Find three consecutive odd integers whose sum is -45.

• -15, -17, -19
• -17, -18, -19
• -13, -15, -17

Multiple Choice

One half of 2 more than 3 times a number is 14 less than twice the number. Find this number.

• 24

• 26

• 28

• 30

Multiple Choice

Which of the following setups would be used to find four consecutive integers?

• n
  n+2
  n+4
  n+6
• n
  2n
  4n
  6n
• n+1
  n+2
  n+3
  n+4
• n
  n+1
  n+2
  n+3

Multiple Choice

The larger of two numbers exceeds the smaller number by 12. If the sum of the two numbers is 74, find the two numbers.

• 12 and 24

• 31 and 43

• 24 and 36

• 51 and 63

Multiple Choice

The sum of three consecutive odd numbers is -27.  What is the largest of the three numbers?

• -7
• -9
• -11
• -13

Multiple Choice

Find three consecutive odd integers whose sum is -45.

• -15, -17, -19
• -17, -18, -19
• -13, -15, -17

Multiple Choice

Find two consecutive integers whose sum is -97.

• -48, 49
• 47, 50
• -49, -50
• -48, -49

Multiple Choice

The larger of two numbers is 10 less than twice the smaller number. If the sum of the two numbers is 38, find the two numbers.

• 16,22

• 10,28

Multiple Choice

Find four consecutive odd integers whose sum is 128.

• 32, 34, 37, 38
• 27, 29, 31, 33
• 29, 31, 33, 35
• 25, 27, 29, 31

Multiple Choice

The sum of three consecutive EVEN numbers is -138.  What is the smallest of the three numbers?

• -48
• -45
• -46
• -47

Multiple Choice

Which expressions can be used to represent the sum of 3 consecutive odd integers?

• n+1, n+2, n+3
• n, n+1, n+3
• n, n+1, n+2
• n, n+2, n+4

Multiple Choice

Find four consecutive odd integers whose sum is 128.

• 32, 34, 37, 38
• 27, 29, 31, 33
• 29, 31, 33, 35
• 25, 27, 29, 31

Multiple Choice

Find three consecutive integers such that the sum of the largest and 5 times the smallest is -244.

• -41, -42, -43
• -41, -43, -45
• -39, -40, -41
• 41, 42, 43

Multiple Choice

Three consecutive even integers are such that the sum of the smallest and 3 times the second is 38 more than twice the third. Find the largest integer.

• 20

• 22

• 24

• 26

Multiple Choice

Find three consecutive even integers whose sum is 84.

• 26, 28, 30
• 28, 30, 32
• 27, 28, 29
• 24, 26, 28

Multiple Choice

Find three consecutive even integers whose sum is 84.

• 26, 28, 30
• 28, 30, 32
• 27, 28, 29
• 24, 26, 28

Multiple Choice

The sum of 4 consecutive even numbers is 364.  What is the sum of the middle two numbers? 

• 91
• 92
• 183
• 182

Multiple Choice

The sum of two consecutive integers is 123.  What is the smallest of the two integers?

• 60
• 61
• 62
• 63

Multiple Choice

The sum of 5 consecutive integers is -240. What are those integers?

• 46, 47, 48, 49 and 50

• -50, -51, -52, -53 and -54

• -50, -49, -48, -47 and -46

• 50, 51, 52, 53 and 54

Multiple Choice

The sum of three consecutive numbers is -30.  What is the smallest of the three numbers?

• -10
• -11
• -12
• -9

Multiple Choice

The sum of three consecutive odd numbers is -27.  What is the largest of the three numbers?

• -7
• -9
• -11
• -13

Multiple Choice

The sum of 4 consecutive even numbers is 364.  What is the sum of the middle two numbers? 

• 91
• 92
• 183
• 182

Multiple Choice

The sum of three consecutive odd integers 141. What are the three integers?

• 47, 48 , 49
• 45, 47, 49
• 46, 48, 50
• 41, 49, 51

Multiple Choice

The sum of three consecutive EVEN numbers is -138.  What is the smallest of the three numbers?

• -48
• -45
• -46
• -47

Fill in the Blanks

Find four consecutive integers such that 6 times the sum of the first and the fourth is 26 less than 10 times the third.

Fill in the Blanks

Find 3 consecutive integers such that twice the sum of the first two is 2 less than 3 times the third.

Fill in the Blanks

Find four consecutive integers such that 8 times the sum of the first and the third is 40 greater than 10 times the fourth.

Fill in the Blanks

There are 10 less trumpet players than saxophone players. The number of saxophone players is 3 times the number of trumpet players. How many trumpet players are there?

Multiple Choice

The length of a rectangle is 5 less than twice its width. The perimeter is 26 meters. Find the dimensions of the rectangle.

• 5 m by 8 m

• 3 m by 10 m

• 4 m by 9 m

• 6 m by 7 m