Print array elements from index k

I have a bash array and want to print the array elements starting from index k.

Things did not work out with the following strategy.

printf "%s\n" "${ar[$j:]}"

The syntax is ${ar[@]:j}¹. From the Parameter Expansion section of man bash:

   ${parameter:offset:length}
   .
   .
   .
          If parameter is an indexed array name subscripted by @ or *, the
          result is the length members of the array beginning  with  ${pa‐
          rameter[offset]}.   A  negative  offset is taken relative to one
          greater than the maximum index of the specified array.  It is an
          expansion error if length evaluates to a number less than zero.

So given

$ ar=("1" "2 3" "4" "5 6" "7 8" "9")

then (remembering that bash array indixing is 0-based):

$ j=3; printf '%s\n' "${ar[@]:j}"
5 6
7 8
9

Alternatively, use a C-style for loop:

for ((i=k;i<${#ar[@]};i++)); do
  printf '%s\n' "${ar[i]}"
done

1. or ${ar[@]:$j} if you prefer - the second $ is optional, since the indices are evaluated in a numerical context similar to ((...))