3-11 Consecutive even/odd
Integers
Consecutive Integers
There are only two formulas to remember to solve these problems
The first one is consecutive integers.
What are consecutive integers?
Consecutive Integers
There are only two formulas to remember to solve these problems
The first one is consecutive integers.
What are consecutive integers?
0
1
2
3
4
5
6
Consecutive Integers
There are only two formulas to remember to solve these problems
The first one is consecutive integers.
What are consecutive integers?
0
1
2
3
4
5
x
x+1
x+2
x+3
x+4
x+5
6
x+6
So the formula for consecutive integers is
x + (x+1) + (x + 2)….. And so on. The number of terms we have depends on
the number the problem asks us to find
Example
The sum of two consecutive integers is 61.
How many numbers do we need?
Example
The sum of two consecutive integers is 61.
How many numbers do we need? 2
So our equation is…
Example
The sum of two consecutive integers is 61.
How many numbers do we need? 2
So our equation is… x +(x + 1) = 61
Example
The sum of two consecutive integers is 61.
How many numbers do we need? 2
So our equation is… x +(x + 1) = 61
2x + 1 = 61
Example
The sum of two consecutive integers is 61.
How many numbers do we need? 2
So our equation is… x +(x + 1) = 61
2x + 1 = 61
-1
-1
2x
= 60
Example
The sum of two consecutive integers is 61.
How many numbers do we need? 2
So our equation is… x +(x + 1) = 61
2x + 1 = 61
-1
-1
2x
2
= 60
2
Example
The sum of two consecutive integers is 61.
How many numbers do we need? 2
So our equation is… x +(x + 1) = 61
2x + 1 = 61
-1
-1
2x
2
X = 30
= 60
2
so x + 1 = 31.
Our integers are 30 and 31
Consecutive Even/Odd
There is only 1 formula to remember for consecutive even and odd as well.
The only difference will be that our x (starting number) will either be even or
odd.
Assume our starting number is odd
Consecutive Even/Odd
There is only 1 formula to remember for consecutive even and odd as well.
The only difference will be that our x (starting number) will either be even or
odd.
Assume our starting number is odd
1
2
3
4
5
6
7
Consecutive Even/Odd
There is only 1 formula to remember for consecutive even and odd as well.
The only difference will be that our x (starting number) will either be even or
odd.
Assume our starting number is odd
1
2
3
4
x
x+1
x+2
x+3
What do you notice about the odd numbers
5
x+4
6
7
x+5
x+6
Consecutive Even/Odd
There is only 1 formula to remember for consecutive even and odd as well.
The only difference will be that our x (starting number) will either be even or
odd.
Assume our starting number is odd
1
2
3
4
x
x+1
x+2
x+3
What do you notice about the odd numbers
x +(x+2) + (x + 4)
5
x+4
6
7
x+5
x+6
Consecutive even/odd
Now lets assume our number is even to start
2
3
4
5
6
7
8
Consecutive even/odd
Now lets assume our number is even to start
2
3
x
x+1
4
x+2
5
6
x+3
x+4
What do you notice about even numbers
7
8
x+5
x+6
Consecutive even/odd
Now lets assume our number is even to start
2
3
x
x+1
4
x+2
5
6
x+3
x+4
7
8
x+5
x+6
What do you notice about even numbers
x + (x+2) + (x +4)
What do you notice about the formula for
consecutive even and odd numbers?
Consecutive even/odd
Now lets assume our number is even to start
2
3
x
x+1
4
x+2
5
6
x+3
x+4
7
8
x+5
x+6
What do you notice about even numbers
x + (x+2) + (x +4)
What do you notice about the formula for
consecutive even and odd numbers?
The formula is the same. x + (x + 2) + (x + 4)
Examples
The sum of three consecutive odd integers is 75. What are the integers.
What’s our formula?
Examples
The sum of three consecutive odd integers is 75. What are the integers.
What’s our formula?
x + (x + 2) + (x + 4) = 75
combine like terms
Examples
The sum of three consecutive odd integers is 75. What are the integers.
What’s our formula?
3x + 6 = 75
x + (x + 2) + (x + 4) = 75
combine like terms
Examples
The sum of three consecutive odd integers is 75. What are the integers.
What’s our formula?
3x + 6 = 75
-6
-6
3x = 69
x + (x + 2) + (x + 4) = 75
combine like terms
Examples
The sum of three consecutive odd integers is 75. What are the integers.
What’s our formula?
3x + 6 = 75
-6
-6
3x = 69
3
3
x + (x + 2) + (x + 4) = 75
combine like terms
Examples
The sum of three consecutive odd integers is 75. What are the integers.
What’s our formula?
x + (x + 2) + (x + 4) = 75
3x + 6 = 75
-6
-6
3x = 69
3
3
X = 23
x+ 2 =
combine like terms
Examples
The sum of three consecutive odd integers is 75. What are the integers.
What’s our formula?
x + (x + 2) + (x + 4) = 75
combine like terms
3x + 6 = 75
-6
-6
3x = 69
3
3
X = 23
x+ 2 = 25
x+ 4 =
Examples
The sum of three consecutive odd integers is 75. What are the integers.
What’s our formula?
x + (x + 2) + (x + 4) = 75
combine like terms
3x + 6 = 75
-6
-6
3x = 69
3
3
X = 23
x+ 2 = 25
x+ 4 = 27
So our 3 consecutive odd integers are 23, 25, 27
Examples
The sum of three consecutive even integers is 66. What are the integers.
What’s our formula?
Examples
The sum of three consecutive even integers is 66. What are the integers.
What’s our formula?
x + (x + 2) + (x + 4) = 66
combine like terms
Examples
The sum of three consecutive even integers is 66. What are the integers.
What’s our formula?
3x + 6 = 66
x + (x + 2) + (x + 4) = 66
combine like terms
Examples
The sum of three consecutive even integers is 66. What are the integers.
What’s our formula?
3x + 6 = 66
-6
-6
3x = 60
x + (x + 2) + (x + 4) = 66
combine like terms
Examples
The sum of three consecutive even integers is 66. What are the integers.
What’s our formula?
3x + 6 = 66
-6
-6
3x = 60
3
3
x + (x + 2) + (x + 4) = 66
combine like terms
Examples
The sum of three consecutive even integers is 66. What are the integers.
What’s our formula?
x + (x + 2) + (x + 4) = 66
3x + 6 = 66
-6
-6
3x = 60
3
3
X = 20
x+ 2 =
combine like terms
Examples
The sum of three consecutive even integers is 66. What are the integers.
What’s our formula?
x + (x + 2) + (x + 4) = 66.
combine like terms
3x + 6 = 66
-6
-6
3x = 60
3
3
X = 20
x+ 2 = 22
x+ 4 =
Examples
The sum of three consecutive even integers is 66. What are the integers.
What’s our formula?
x + (x + 2) + (x + 4) = 66
combine like terms
3x + 6 = 66
-6
-6
3x = 60
3
3
X = 20
x+ 2 = 22
x+ 4 = 24
So our 3 consecutive even integers are 20, 22, 24
Try This
The sum of two consecutive odd integers is 76. What are the integers?
The sum of two consecutive even integers is 106. What are the integers?
The sum of three consecutive integers is 126. What are the integers?
The sum of three consecutive odd integers is 189. What are the integers?