What exactly is Excel's Auto Fill algorithm?

What is the algorithm used by Auto Fill in Excel?

For example, when I enter the numbers 3,4,5,7,8 into a column and then use Auto Fill, I get the following result:

 3
 4
 5
 7
 8
 9.3
10.6
11.9
13.2
14.5
15.8
17.1
18.4

Excel uses its Linear Trend approach when you auto-fill. This employs the least-squares method algorithm.

This is the same algorithm used by the TREND() function as seen demonstrated below:

Enter the following formula in C6 and ctrl-enter/copy-paste/fill-down into the rest of the column:

=TREND($C$1:$C$5,$B$1:$B$5,B6)

Below is a chart showing the trend line that the new values fall on.

The least-squares method creates a "best fit" line for the original data points. The new data points are essentially extracted from this line.