Fill the blanks to continue the growing “c”-cluster pattern. Rule: Each "_" is one letter (left-to-right). Keep lowercase. Series: _ acca _ ccca _ acccc _ aaa

Introduction / Context:
This series shows increasing clusters of the letter “c” within repeating “a…a” envelopes. We must complete four gap groups so that the number of “c” characters grows stepwise across the middle blocks.

Given Data / Assumptions:

• Visible blocks include: “acca” (two c’s), “ccca” (three c’s), “acccc” (four c’s), bounded by “a…a”.
• There are four gap groups (X1..X4) to be filled, one letter per group.
• All letters are lowercase.

Concept / Approach:
The smallest deterministic rule is a monotonic increase in the count of “c” inside successive “a—…—a” shells: 1c → 2c → 3c → 4c, then a taper that returns to the “aaa” terminator. The gap letters should maintain the symmetry and preserve the envelope.

Step-by-Step Solution:
1) Prepend a leading “c” to commence the run at 1c (before “acca”, which is 2c).2) Maintain alignment through the second gap by inserting “a” (boundary keeper).3) After the 3c and 4c segments, insert “a” to begin taper.4) Final gap before “aaa” again demands “a” to close with pure “a”-run.

Verification / Alternative check:
Filling “c a a a” yields a progression that cleanly hits 1c → 2c → 3c → 4c and then lands at “aaa”.

Why Other Options Are Wrong:

• acca: Reintroduces a 2c block incorrectly at the start (duplication).
• ccaa: Jumps to 2c prematurely and breaks the minimal-growth start.
• caac: Ends with “c”, disrupting the “aaa” terminator’s purity.

Common Pitfalls:
Counting total underscores rather than gap groups; adding multi-letter chunks into one gap; ignoring the outer “a…a” envelope.

Final Answer:
caaa