Series Completion: 5824, 5242, ?, 4247, 3823

Concept

Some number series follow a digit-decomposition rule rather than a constant addition/multiplication step: each term is produced by taking the previous term and subtracting from it the number formed by its own leading digits. Spotting which digits are used, and confirming the rule holds across every consecutive pair, is the key skill.

Application

1. Check the first pair: from 5824, take its leading three digits (582) and subtract: 5824 - 582 = 5242, which matches the given second term.

2. Apply the same rule to 5242: take its leading three digits (524) and subtract: 5242 - 524 = 4718. This is the missing term.

3. Continue the rule with 4718: its leading three digits are 471, so 4718 - 471 = 4247, matching the next given term.

4. Continue once more with 4247: its leading three digits are 424, so 4247 - 424 = 3823, matching the final given term.

Cross-check

Applying this single rule step by step reproduces every given term of the series (5824 -> 5242 -> ? -> 4247 -> 3823) without any adjustment, so 4718 is confirmed as the consistent missing term, not just a value that happens to fit locally.