The next term in the sequence $1, 4, 9, 16$ is $25$.

This sequence consists of the squares of consecutive natural numbers. Let’s analyze it step by step: the first term is $1$, which equals $1^2$; the second term is $4$, corresponding to $2^2$; the third term is $9$, which is $3^2$; and the fourth term is $16$, represented as $4^2$. Following this established pattern, the next term will be the square of the subsequent natural number, which is $5$. Thus, we find that $5^2 = 25$.

In general, when you encounter a sequence and need to determine the next term, it is beneficial to identify any underlying patterns. In this case, recognizing that each term is a perfect square allows us to predict the next term effectively. Sequences of this nature are commonly referred to as quadratic sequences, as their terms are derived from squaring integers. Grasping these types of patterns can greatly assist you in solving similar problems during your GCSE Maths examinations.