– ALGEBRA I – Unit 1 – Section 2

Consecutive Integer Problems

In order to work with a “consecutive integer”

problems, we need to start by understanding the

terminology:

Consecutive Consecutive means: “In a row” or “In order.”

– ALGEBRA I – Unit 1 – Section 2

Consecutive Integer Problems

In order to work with a “consecutive integer”

problems, we need to start by understanding the

terminology:

Integer An integer is: a nice, round, positive/negative

number.

– ALGEBRA I – Unit 1 – Section 2

Consecutive Integer Problems

The key thing to remember is that your answers will be

consecutive integers. In other words, the numbers you get should be “nice” (a.k.a. no

fractions or decimals) and they should be in a row.

Let’s go through

some examples.

Example ProblemsConsecutive Integer Problem

The sum of three consecutive integers is 51. Find the numbers

• The first thing to note is that we are dealing with consecutive integers. • An example (that is not necessarily the solution) of

consecutive integers could be: 20 21 22

Notice that to get from the first number in the list to the second, we need to add 1.

+1

Example ProblemsConsecutive Integer Problem

The sum of three consecutive integers is 51. Find the numbers

• The first thing to note is that we are dealing with consecutive integers. • An example (that is not necessarily the solution) of

consecutive integers could be: 20 21 22

To get from the first number in the list to the third, we need to add 2.

+1 +2

Example ProblemsConsecutive Integer Problem

The sum of three consecutive integers is 51. Find the numbers

• Instead of using numbers, we need to switch to variables.

20 21 22+1 +2

N• Note that we follow the same “addition” procedure.

+1 +2

N + 1 N + 2

Example ProblemsConsecutive Integer Problem

The sum of three consecutive integers is 51. Find the numbers

• Now to start the problem, we begin by writing the expressions for the THREE integers:

N• Since we are looking for the sum, the equation is:

N + 1 N + 2

N + N + 1 + N + 2 = 51

Example ProblemsConsecutive Integer Problem

The sum of three consecutive integers is 51. Find the numbers

• Suppose that the possible solutions for the first number are 15, 16, or 17. Guess and test to solve:

(15) + (15) + 1 + (15) + 2 = 15 + 16 + 17 = 48 51

(16) + (16) + 1 + (16) + 2 = 16 + 17 + 18 = 51 = 51

(17) + (17) + 1 + (17) + 2 = 17 + 18 + 19 = 54 51

Example ProblemsConsecutive Integer Problem

The sum of three consecutive integers is 51. Find the numbers

• Since 16 is the solution for the FIRST number in the list, the complete solution is:

N = 16

N + 1 = 16 + 1 = 17

N + 2 = 16 + 2 = 18

Notice that the 3 solutions are integers, add up to 51, and are consecutive.

Example ProblemsConsecutive EVEN Integer Problem

The sum of three consecutive EVEN integers is 84. Find the numbers

• The first thing to note is that we are dealing with consecutive EVEN integers. • An example (that is not necessarily the solution) of

consecutive integers could be: 20 22 24

Notice that to get from the first number in the list to the second, we need to add 2.

+2

Example ProblemsConsecutive EVEN Integer Problem

The sum of three consecutive EVEN integers is 84. Find the numbers

• The first thing to note is that we are dealing with consecutive integers. • An example (that is not necessarily the solution) of

consecutive integers could be: 20 22 24

To get from the first number in the list to the third, we need to add 4.

+2 +4

Example ProblemsConsecutive EVEN Integer Problem

The sum of three consecutive EVEN integers is 84. Find the numbers

• Instead of using numbers, we need to switch to variables.

20 22 24+2 +4

N• Note that we follow the same “addition” procedure.

+2 +4

N + 2 N + 4

Example ProblemsConsecutive EVEN Integer Problem

The sum of three consecutive EVEN integers is 84. Find the numbers

• Now to start the problem, we begin by writing the expressions for the THREE integers:

N• Since we are looking for the sum, the equation is:

N + 2 N + 4

N + N + 2 + N + 4 = 84

Example ProblemsConsecutive EVEN Integer Problem

The sum of three consecutive EVEN integers is 84. Find the numbers

• Suppose that the possible solutions for the first number are 22, 24, or 26. Guess and test to solve:

(22) + (22) + 1 + (22) + 2 = 22 + 24 + 26 = 72 84

(24) + (24) + 1 + (24) + 2 = 24 + 26 + 28 = 78 84

(26) + (26) + 1 + (26) + 2 = 26 + 28 + 30 = 84 = 84

Example ProblemsConsecutive EVEN Integer Problem

The sum of three consecutive EVEN integers is 84. Find the numbers

• Since 26 is the solution for the FIRST number in the list, the complete solution is:

N = 26

N + 2 = 26 + 2 = 28

N + 4 = 26 + 4 = 30

Notice that the 3 solutions are integers, even, add up to 84, and are consecutive.

Example ProblemsConsecutive ODD Integer Problem

The sum of three consecutive ODD integers is 57. Find the numbers

• The first thing to note is that we are dealing with consecutive ODD integers. • An example (that is not necessarily the solution) of

consecutive integers could be: 21 23 25

Notice that to get from the first number in the list to the second, we need to add 2.

+2

Example ProblemsConsecutive ODD Integer Problem

The sum of three consecutive ODD integers is 57. Find the numbers

• The first thing to note is that we are dealing with consecutive integers. • An example (that is not necessarily the solution) of

consecutive integers could be: 21 23 25

To get from the first number in the list to the third, we need to add 4.

+2 +4

Example ProblemsConsecutive ODD Integer Problem

The sum of three consecutive ODD integers is 57. Find the numbers

• Instead of using numbers, we need to switch to variables.

21 23 25+2 +4

N• Note that we follow the same “addition” procedure.

+2 +4

N + 2 N + 4

Example ProblemsConsecutive ODD Integer Problem

The sum of three consecutive ODD integers is 57. Find the numbers

• Now to start the problem, we begin by writing the expressions for the THREE integers:

N• Since we are looking for the sum, the equation is:

N + 2 N + 4

N + N + 2 + N + 4 = 57

Example ProblemsConsecutive ODD Integer Problem

The sum of three consecutive ODD integers is 57. Find the numbers

• Suppose that the possible solutions for the first number are 17, 19, or 21. Guess and test to solve:

(17) + (17) + 1 + (17) + 2 = 17 + 19 + 21 = 57 = 57

(19) + (19) + 1 + (19) + 2 = 19 + 21 + 23 = 63 57

(21) + (21) + 1 + (21) + 2 = 21 + 23 + 25 = 69 57

Example ProblemsConsecutive ODD Integer Problem

The sum of three consecutive ODD integers is 57. Find the numbers

• Since 17 is the solution for the FIRST number in the list, the complete solution is:

N = 17

N + 2 = 17 + 2 = 19

N + 4 = 17 + 4 = 21

Notice that the 3 solutions are integers, odd, add up to 57, and are consecutive.

Try This Problem…Use the procedures that we just

went through to the solve the following problems.

1. The sum of four consecutive even integers is 268. Find the numbers. (Possible solutions for the first number: 60, 64, or 70)

**The answers can be found at the end of the PowerPoint.

2. The product of two consecutive odd integers is 143. Find the numbers. (Possible solutions for the first number: 9, 11, or 13)

ALGEBRA IS FUN

AND EASY!**Answers: 1) 64, 66, 68, and 70 2) 11 and 13