Complete the sequence: 1, 11, 21, 1211, 111221, ____ (identify the next term in the standard “look-and-say” sequence).

Introduction / Context:
This is the classic “look-and-say” (run-length encoding) sequence. Each term describes the previous term by counting contiguous runs of identical digits, then saying the digit. You must generate the next term from 111221.

Given Data / Assumptions:

• Sequence so far: 1, 11, 21, 1211, 111221.
• Rule: read off the prior term as counts followed by digit.

Concept / Approach:
Break 111221 into contiguous runs: “111” (three 1s), “22” (two 2s), “1” (one 1). Convert each run to count+digit and concatenate: “31” for three 1s, “22” for two 2s, “11” for one 1, giving 312211.

Step-by-Step Solution:
1) Identify runs: 111 / 22 / 1.2) Encode: 111 → 31; 22 → 22; 1 → 11.3) Concatenate: 31 22 11 → 312211.

Verification / Alternative check:
Check back one step: 1211 → read as “one 1, one 2, two 1s,” i.e., 111221, confirming the mechanism you just applied forward.

Why Other Options Are Wrong:
They miscount runs or reorder digits, which violates the deterministic rule.

Common Pitfalls:
Counting total occurrences rather than contiguous runs. The rule always applies to contiguous blocks.

Final Answer:
312211