To determine the next term in this sequence, we need to analyze the pattern and rules that govern its progression.
The sequence starts with 1. The next term, 11, can be described as "one 1," since it consists of two consecutive 1s. The following term, 21, can be described as "two 1s," as it consists of one 2 and one 1.
Continuing this pattern, the next term is 1211, which can be described as "one 2, one 1."
The pattern continues in this manner, where each term is described in terms of the counts of consecutive digits in the previous term.
Now, let's go through each option and determine which one follows this pattern:
A. 112221: This option does not follow the pattern. It does not describe the counts of consecutive digits in the previous term.
B. 131221: This option does not follow the pattern. It does not describe the counts of consecutive digits in the previous term.
C. 312211: This option follows the pattern. It describes the counts of consecutive digits in the previous term (one 3, one 1, two 2s, one 1).
D. 221221: This option does not follow the pattern. It does not describe the counts of consecutive digits in the previous term.
Therefore, the correct answer is C. 312211.