When I’m doing coding interviews I always like to start off and say I’m a big fan of very long variable names. “As descriptive as you can be” I say. Then I get to my first for loop. Instead of i I use “iterator” and then when I start a nested loop I use “jiterator” and it always gets a laugh.

i is for index. j is simply the next letter and we’re too lazy to think up something meaningful

It depends. x and y are either elements or coordinates, a and b usually elements though in e.g. Haskell reserved (by convention) for type variables.

The i j k l series is reserved for indices. n m etc. are the counts of something, as such you’ll see i counting up to n. Both are due to mathematical sum notation and general mathematical convention. Random google result:

Let x₁, x₂, x₃, …x_n denote a set of n numbers. x₁ is the first number in the set. x_i represents the ith number in the set.

…if you’re using a language in which you use i often chances are you should stop coding in C and get yourself a language with iterators. Manual loops are a bug magnet.

A useful tip I picked up was to use ii instead of j for an inner loop. It’s far more distinct than j.

If for some terrible reason you have even more inner loops you can easily continue the trend i, ii, iii, iiii, iiiii - or iv, v if you’re feeling roman