In the following series some letters are missing which are given in that order…

Concept

A letter-completion series of this kind is built by repeating one fixed block of letters end to end. Some positions are blanked out; the missing letters are exactly the characters that the repeating block places at those positions. So the method is: discover the period (the length of the block that repeats), then read off whatever the block must contain at each blank.

Application

Write the series with its gaps and number every position from 1:

aac _ a _ cbab _ b _ accab _ ba _ cb

There are 24 positions and six blanks, at positions 4, 6, 11, 13, 19 and 22. Counting the visible letters shows the string is made of two equal halves of 12, so the repeating block has length 12. Aligning the two halves position by position lets each blank be filled from the matching position in the other half:

1. Position 4 sits opposite a 'c' in the second half → c

2. Position 6 sits opposite a 'b' → b

3. Position 11 sits opposite a 'c' → c

4. Position 13 sits opposite an 'a' → a

5. Position 19 sits opposite a 'c' → c

6. Position 22 sits opposite a 'b' → b

Reading the six filled letters in their blank order gives c, b, c, a, c, b — that is "cbcacb".

Cross-check

Substitute them back in. The completed series becomes aaccabcbabcb aaccabcbabcb — the single 12-letter block “aaccabcbabcb” written twice with nothing left over. The two halves are identical, which is exactly the periodicity the puzzle demands, so the missing letters are cbcacb.