- The given letter series is "a_b_a_ _n_bb_abbna".
- We need to find the set of letters that can be placed sequentially at the gaps to complete the series.
- Let's analyze the given series step by step to determine the pattern and find the missing letters.

1. "a_b_a_ _n_bb_abbna"

- The first gap is between the letters "a" and "b". We can see that the letter "b" is repeated in the series. So, let's try placing "b" in the first gap.

2. "ab_a_ _n_bb_abbna"

- The second gap is between the letters "a" and "n". We can see that the letter "n" is also repeated in the series. So, let's try placing "n" in the second gap.

3. "abnan_ _n_bb_abbna"

- The third gap is between the letters "n" and "b". We can see that the letter "b" is repeated in the series. So, let's try placing "b" in the third gap.

4. "abnanb_n_bb_abbna"

- The fourth gap is between the letters "b" and "b". We can see that the letter "b" is repeated in the series. So, let's try placing "b" in the fourth gap as well.

5. "abnanbnb_bb_abbna"

- The fifth gap is between the letters "b" and "a". We can see that the letter "a" is repeated in the series. So, let's try placing "a" in the fifth gap.

6. "abnanbnbabb_abbna"

- The sixth gap is between the letters "a" and "b". We can see that the letter "b" is repeated in the series. So, let's try placing "b" in the sixth gap.

7. "abnanbnbabbnabbna"

- The seventh gap is between the letters "b" and "n". We can see that the letter "n" is repeated in the series. So, let's try placing "n" in the seventh gap.

- After placing the letters sequentially at the gaps, we get the completed series as "abnanbnbabbnabbna".

Therefore, the correct set of letters that completes the given series is "bnbban" which is option B.