Age of Information (AoI) has emerged as a key metric for assessing data freshness in IoT applications, where a large number of devices report time-stamped updates to a monitor. Such systems often rely on random access protocols based on variations of ALOHA at the link layer, where collision resolution algorithms play a fundamental role to enable reliable delivery of packets. In this context, we provide the first analytical characterization of average AoI for the classical Capetanakis tree-based algorithm with gated access under exogenous traffic, capturing the protocol's dynamics, driven by sporadic packet generation and variable collision resolution times. We also explore a variant with early termination, where contention is truncated after a maximum number of slots even if not all users are resolved. The approach introduces a fundamental trade-off between reliability and timeliness, allowing stale packets to be dropped to improve freshness.