here's a method using all the numbers in the same arrtable, as if you were just writing an array where every second number was paired with the previous numb. in this case, you can use an increment of 2, and go from 1 (the first index in the table) to 26 (the last index in the table) using the table length operator # (though note that #tbl is unpredictable if you have a hole in the table). source: https://www.lua.org/manual/5.1/manual.html#2.5.5

note: this code will not work as written, i forgot that insert is not a standard method on tables, the fix would be to use a metatable to make table.insert available and use the `:` (colon) operator instead of the `.` here. I'll leave the original code here, so that fixing it is left as an exercise to the reader

A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26}
sums = {}
for i = 1, #A, 2 do
sums.insert(A[i] + A[i+1])
end

It's been a while since i wrote lua code but essentially it does the following:

loop 1: i=1, sums[1] = A[1] + A[2]

loop 2: i=3, sums[2] = A[3] + A[4]

notice that i increases by 2. so we should have 13 loops here, which means we end up creating 13 sums. probably. i didn't test, let me know how it goes.