Consecutive Numbers
Algebra I
Consecutive Integers

are numbers in
counting orders
Examples
-3, -2, -1, 0, 1, 2, 3

---|-----|------|-----|------|-----|-----|-----|-----|-----|-----|-----|-----|-----|---
-2
-1
0
1
2
3
4
5
6
7
8
9
10
11
---|-----|------|-----|------|-----|-----|-----|-----|-----|-----|-----|-----|-----|---
-2 -1 0
1
2 3 4 5 6
7 8 9 10 11
When counting
CONSECUTIVE
integers, You will…
Add by 1’s
Ex + 1, + 2, + 3

When counting
CONSECUTIVE ODD
OR EVEN integers,
you will …
Add by 2’s
Ex + 2, + 4, + 6, + 8

Examples
1) The sum of two consecutive integers is 17. Find the two numbers.
x+0
» represents 1st number
x+1
» represents 2nd number
2x + 1 = 17
-1
-1
2x
= 16
2
2
X=8
add 1st and 2nd number together and set equal to 17. Solve.
Now x + 0
becomes
8 + 0 which is 8
Now x +1
becomes
8 + 1 which is 9
Check
8 + 9 = 17
Examples
2) The sum of three consecutive integers is 129. Find the three numbers.
x+0
» represents 1st number
x+1
» represents 2nd number
x+2
» represents 3rd number
3x + 3 = 129
-3
3x
add 1st, 2nd & 3rd number together and set equal to 129. Solve.
-3
= 126
3
3
X=42
Now x + 0
becomes
42 + 0 which is 42
Now x +1
becomes
42 + 1 which is 43
Now x + 2
becomes
42 + 2 which is 44
Check
42 + 43 + 44 =129
Examples
3) The sum of four consecutive integers is -334. Find the four numbers.
x+0
» represents 1st number
x+1
» represents 2nd number
x+2
» represents 3rd number
x+3
» represents 4th number
4x + 6 = -334 add 1st, 2nd , 3rd & 4th number together and set equal to -334. Solve.
-6
4x
-6
= -340
4
4
X=-85
Now x + 0
becomes
-85 + 0 which is -85
Now x +1
becomes
-85 + 1 which is -84
Now x + 2
becomes
-85 + 2 which is -83
Now x + 3
becomes
-85 + 3 which is -82
Check
-85 + -84 + -83 + -82 = -334
Examples
4) The sum of three consecutive integers is 105. Find the three numbers.
x+0
» represents 1st number
x+1
» represents 2nd number
x+2
» represents 3rd number
3x + 3 = 105
-3
3x
add 1st, 2nd & 3rd number together and set equal to 105. Solve.
-3
= 102
3
3
X=34
Now x + 0
becomes
34 + 0 which is 34
Now x +1
becomes
34 + 1 which is 35
Now x + 2
becomes
34 + 2 which is 36
Check
34 + 35 + 36 = 105
Examples
5) The sum of three consecutive even integers is 396. Find the three numbers.
x+0
» represents 1st number
x+2
» represents 2nd number
x+4
» represents 3rd number
3x + 6 = 396
-6
3x
add 1st, 2nd & 3rd number together and set equal to 396. Solve.
-6
= 390
3
3
X=130
Now x + 0
becomes
130 + 0 which is 130
Now x +2
becomes
130 + 2 which is 132
Now x + 4
becomes
130 + 4 which is 134
Check
130 + 132 + 134 = 396
Examples
6) The sum of four consecutive even integers is 138. Find the four numbers.
x+0
» represents 1st number
x+2
» represents 2nd number
x+4
» represents 3rd number
x+6
» represents 4th number
4x + 12 = 138 add these number together and set equal to 138. Solve.
-12
4x
4
-12
= 126
4
X=31.5
No solution: Must be whole number
Examples
7) The sum of three consecutive odd integers is 285. Find the three numbers.
x+0
» represents 1st number
x+2
» represents 2nd number
x+4
» represents 3rd number
3x + 6 = 285
-6
3x
add 1st, 2nd & 3rd number together and set equal to 285. Solve.
-6
= 279
3
3
X=93
Now x + 0
Now x + 2
Now x + 4
becomes
93 + 0 which is 93
becomes 93 + 2 which is 95
becomes
Check
93 + 95 + 97 = 285
93 + 4 which is 97
Examples
8) The sum of four consecutive odd integers is 0. Find the four numbers.
x+0
» represents 1st number
x+2
» represents 2nd number
x+4
» represents 3rd number
x+6
» represents 4th number
4x + 12 = 0 add these number together and set equal to 0. Solve.
-12 -12
4x
= -12
4
4
X=-3
Now x + 0
Now x + 2
Now x + 4
Now x + 6
Check
-3 + -1 + 1
becomes
becomes
becomes
becomes
+3 =0
-3
-3
-3
-3
+
+
+
+
0
2
4
6
which
which
which
which
is
is
is
is
-3
-1
1
3