Given a sequence: 3, 7, 11, 15
Convert to a table
X Y
1
2
3
4
3
7
11
15
Determine the common X difference and the common Y difference
X Y
1
2
3
4
Rack ‘em
by putting the y difference
over
the x difference
3
7
11
15
4
1
in this case 4 / 1 or 4
The equation begins y = mx + b
We now have
y = 4x + b
To find the y-intercept we are looking for (0,b)
So lets back up just one step in our sequence to X=0
X
0
1
2
3
4
Y
3
7
11
15
Then the Y can easily be determined as
X Y
0 -1
1 3
2 7
3 11
4 15
This completes the equation that generates the sequence 3,7,11,15
Y = 4x + (-1)
Or simply
Y = 4x -1