I want to use a figure in a field to supplement x in a function,

2x-1, (sin x)/x, or something.

what I have to do is type in some numbers in column A1 to An.

then the awnser B1 to Bn.

First an explanation on the $ symbol. This makes a reference absolute for paste and fill operations. If you have the reference A$1 in a formula, row-1 will not be translated if you use this formula for pasting/filling in a different row. This means you don't want to use an absolute reference for the row.

Now for addressing your problem, try using the Fill Range function. Its in the menu under Edit : Fill Range.

Say for example you want to use the formula 2x-1, where x is in the A column and the result is in the B column. Also assume for this example you are using rows 1 through 10. Enter the following...

Formula: =2*A1+1

Range: B1:B10

This will fill in your B column. Then you only need to enter in your values in the A column. If you are entering a known sequence in the A column you can use the Fill Sequence dialog (its in the menu right under the fill range dialog).

Another trick, if you have a formula for the values in the A column you can use the fill range dialog for this too. For example, if you want integer values from 1 to 10, you can enter 1 in A1. Then use the Fill Range dialog with the following...

Formula: =A1+1

Range: A2:A10

The cool thing about this is, you can change A1 and all of your A values will update. This means you can switch the range from 11 to 20 my simply changing A1 to 11.

Oh, and here is one more trick. You can have the range automatically detected for the Fill Range dialog by selecting the range you want first. If you have a selection it uses this as the initial value for many of the dialogs.

This is only one way you can solve your problem. There are a ton of other ways. You could use copy/paste, etc....