Google sheets convenience question: consolidating a function

Question

This might be closer to a math question with a stupidly easy answer, but I can't figure out the order of functions to use in my cells.

I am trying to find the sum of the absolute values of the differences between two columns of four rows each. A bit of a mouthful, but hopefully the formula I have explains it well enough. =SUM(ABS(A1-B1)+ABS(A2-B2)+ABS(A3-B3)+ABS(A4-B4)) This formula gives me the exact answer I am looking for.

The issue is that I will need to use this formula for hundreds of rows, meaning I would have to type out +ABS(Ax-Bx), x being the row number, hundreds of times. I don't want to do that. Is there a way I can rewrite the function (either mathematically or in terms of google sheets functions) so that I only have to input, say a range and avoid having to type out 100 ABS functions?

I would also accept some easy way to type out 100 copies of ABS(Ax-Bx) with an ascending x value so I can just copy and paste it into the function.

Answer 1

What you need is an array formula, which is designed for just this kind of problem. It lets you apply a formula to every row in a range. There are lots of tutorials online, but here’s a link to the official documentation.