How do I get libreoffice to extrapolate a pattern with an increasing # of terms down a column?

So, I have a column of numbers. I want to create another column of numbers that starts at 1/2 the value and increases at 1/2 the rate.

To do this, I simply brought out the difference between each term in that first column by using =B2-B2,=B3-B2 and put it, say, in column D. Then in the column that I want to generate from these numbers, I use in, say column F: [1/2 the number in the first row of the first column], then F1+(D1/2) then F1+(D1/2)+(D2/2) then F1+(D1/2)+(D2/2)+(D3/3) of course where D contains the difference between corresponding rows in the first, initial column. Therefore, by taking the initial value (in F1) and adding the difference between the corresponding first two rows in the initial column, divided by two, I create a curve that increases at 1/2 the rate.

The problem is, libre-office always generates an extrapolation that does NOT increase the number of terms in each row - it always finds a pattern that WOULD be correct - it advances all of the D references by one row - but alas it never ADDs the d value - it only advances them.

I really really don’t want to enter this by hand… how might one create the desired effect?
Any help is really appreciated.

I think something like =$F$1+SUMPRODUCT(D$1:D1/2) should help. When dragged/copied down only :D1 is changed.