To solve this question, we need to analyze the given letter series and identify the pattern in order to find the missing letters. Let's break down the letter series given:

ab_b_cbacba_ba_cabcba

Observations:
- The series consists of a combination of letters 'a', 'b', and 'c'.
- There are several gaps in the series where a letter is missing.
- The missing letters need to be identified in order to complete the series.

Analyzing the pattern:
- Looking at the series, we can observe that the first letter 'a' remains constant throughout the entire series.
- The second letter 'b' appears at regular intervals, alternating with the letter 'c'.
- The third letter 'c' also appears at regular intervals, alternating with the letter 'b'.

Based on these observations, we can deduce the pattern in the series as follows:

Pattern:
- The first letter 'a' remains constant throughout.
- The second letter alternates between 'b' and 'c'.
- The third letter alternates between 'c' and 'b'.

Finding the missing letters:
- Now, let's identify the missing letters in the series by following the pattern:

ab_b_cbacba_ba_cabcba

- The first gap is between 'a' and 'b'. Following the pattern, the missing letter should be 'c'.
- The second gap is between 'b' and 'c'. Following the pattern, the missing letter should be 'a'.
- The third gap is between 'c' and 'b'. Following the pattern, the missing letter should be 'a'.
- The fourth gap is between 'b' and 'a'. Following the pattern, the missing letter should be 'c'.
- The fifth gap is between 'a' and 'b'. Following the pattern, the missing letter should be 'c'.

Completing the series:
By filling in the missing letters, the completed series becomes:

abcacbcbacbabacabcba

Therefore, the correct set of letters that completes the series is option 'C' (cabac).