Weighted Average Function for Series Weighted by Increments of 1

Excel amateur here..

Is there a way to calculate a weighted average for a series of numbers where each value in the series is increasingly weighted by a value of 1? An example would be:

=(A1+(A2*2)+(A3*3))/1+2+3

...however, I would like it to be in the form of a saved function so that it becomes dynamic enough to apply the logic to any series of numbers of varying length and cell positions. I also want the series of weights (i.e., 1, 2, 3...) to be inherent, without having to create a second array for weights every time this calculation is needed.

Thanks.