How to SUM columns using a variable limit

Could someone please suggest a neat way of using SUM with a variable column range.

I want the result of the sum to appear in Sheet 1 Row 1 Column A. The amounts to be summed are in Sheet 1 Row 1 Columns B to x where x is defined by an integer or long (not a letter) in Sheet 2 Cell A1. Assume it's any number from 1 upwards.

So, if the integer is 1 then the SUM will be B1:B1; if the integer is 2 then the SUM will be B1:C1; if 3 then B1:D1 and 4, B1:E1 and so on.

I hope that makes sense! I just need a tidy way of expressing it.

Thanks.

I wish you were my neighbour! Brilliant, as always. Thank you again!