In the following letter series with blanks, select the set of letters that, when placed sequentially in the gaps, will complete the pattern: a_ ca_c_dc_d_ad_.

Introduction / Context:
This problem involves completing a partially filled letter pattern. You are given a fixed sequence with several blanks and a few answer choices, each of which provides a specific set of letters. The task is to determine which set of letters, when inserted into the blanks in order, produces a meaningful and regular repeating pattern.

Given Data / Assumptions:

• Base pattern with blanks: a_ ca_c_dc_d_ad_
• Four answer options, each a sequence of six letters, to fill the six blanks in order.
• Letters must be inserted sequentially from left to right, using each option string exactly once.
• We look for a smooth, repetitive and consistent pattern after filling the gaps.

Concept / Approach:
We must test each answer option by inserting its letters into the blanks and then checking whether the resulting full sequence displays a simple and regular pattern. A good pattern usually looks repetitive and structured, such as repeating three-letter segments. Once we find such a pattern, we can confidently select that option as the correct one.

Step-by-Step Solution:
Step 1: Remove spaces from the original pattern to observe a continuous sequence: a_ca_c_dc_d_ad_. Step 2: Identify the positions of the six blanks. They occur at fixed positions, and the letters from any chosen option will be placed in these positions in order. Step 3: Try option A (ddacdc). After substitution the resulting string does not form a simple repeated unit and appears irregular. Step 4: Try option B (daadca). The completed string again fails to show a clear repeating cycle. Step 5: Try option C (dadaac). The outcome is still not a neat repetition of a simple block. Step 6: Try option D (ddaacc). Substituting these letters yields the complete sequence: adcadcadcadcadc. Step 7: Observe that this final string is made of the three-letter block "adc" repeated five times: adc adc adc adc adc. This is a very clean, regular and clearly intended pattern.

Verification / Alternative check:
After inserting the letters from option D, we clearly see a repeated cycle of "adc" throughout. None of the other options generate such a neat repetition; they result in uneven and non-repetitive sequences. Because exams typically aim for simple identifiable patterns, a continuous repetition of a three-letter block is strong evidence that we have found the correct answer.

Why Other Options Are Wrong:
Option A (ddacdc): The filled sequence does not break cleanly into a repeated three-letter unit and looks irregular. Option B (daadca): Produces an inconsistent pattern with no obvious repeating segment. Option C (dadaac): Also fails to generate a simple regular pattern; the sequence becomes visually complex with no clear cycle.

Common Pitfalls:
A common mistake is to try to reason position-wise without fully writing out the completed sequence for each option. Another pitfall is to accept a partially repetitive sequence when a perfectly repetitive one exists. For these letter-series completion questions, always check if one option yields a very clear repetitive cycle before deciding.

Final Answer:
The set of letters that completes the series into a neat repeating pattern is ddaacc, which is option D.