Sum of a variable number of cells

Hi and thanks for reading this.
I have a column (say A) with values, say 100 or so. I am trying to make the sum of a number of cells that I input in another cell (say C1). So if C1 contains the number 5 I would like the sums of A1 through A5 to appear, ideally in cell B5, the sum of A6 through A10 in B10 and so on.
I’ve been trying conditional statements with MOD but I can’t figure out how to formulate the range to be summed up.
I’m grateful for any pointers.

The OFFSET function calculates range areas by position and size: Spreadsheet Functions
t79261.ods (13.3 KB)

Awesome! Thanks a bunch.