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Default Define a range end based upon current cell location?

Is there a way to define a range based upon the current cell location? For
instance When I'm calculating a formula in C3 I want to use the range A1:A3,
but when I move down to C4, I want the range to be A1:A4.

The top of the range will remain constant, but the bottom of the range will
move based upon the row I'm currently in.
 
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