In the following question, which one set of letters when sequentially placed at the gaps in the given letter series shall complete it?
a_b_a_c_a_bc

Let's count the total number of characters including gaps, which is 12. We can divide this into 4 groups of 3 elements each:
a _ b∣_ a _∣c _ a∣_ b c
Let's test Option A (bccbb):

First gap: b → abc

Second gap: c → cab

Third gap: c → bca

Fourth gap: b → cab

Fifth gap: b → bbc
This does not form a uniform repeating sequence.

Let's test Option C (cabca):

First gap: c → acb

Second gap: a → aba

Third gap: b → abc
This does not follow a clear cyclic pattern.

Let's examine a cyclic repeating pattern of abc, bca, cab:

If we place the letters from Option B (bcbca):

a [b] b∣[c] a [b]∣c [c] a∣[a] b c
→ inconsistent.

Let's test Option D (acbcb):

First gap: a → aab

Second gap: c → cac

Third gap: b → abc
This is inconsistent.

Let's look closely at Option C (cabca) again with a 3-letter block division:

a [c] b∣[a] a [b]∣c [c] a∣[a] b c
Let's look at a 4-letter grouping pattern instead:

a _ b _∣a _ c _∣a _ b c
If we check Option A (bccbb):

a [b] b [c]∣a [c] c [b]∣a [b] b c
This gives blocks: abbc, accb, abbc. The pattern alternates the middle double letters between bb and cc while keeping the outer letters a and c.

Block 1: a b b c

Block 2: a c c b

Block 3: a b b c

This forms a perfect symmetric alternating pattern. Therefore, the required set of letters is bccbb.