What is the pattern in the sequence 4, 9, 16, 25?

The pattern in the sequence 4, 9, 16, 25 is that each number is a perfect square of consecutive integers.

To understand this pattern better, let's break it down. A perfect square is a number that can be expressed as the product of an integer with itself. For example, 4 is a perfect square because it is 2 multiplied by 2 (2²). Similarly, 9 is 3 multiplied by 3 (3²), 16 is 4 multiplied by 4 (4²), and 25 is 5 multiplied by 5 (5²).

In this sequence, each term is the square of consecutive integers starting from 2. So, the first term is 2², the second term is 3², the third term is 4², and the fourth term is 5². If we continue this pattern, the next term would be 6², which is 36.

Recognising patterns like this is useful in mathematics because it helps us predict future terms in a sequence and understand the relationships between numbers. In this case, knowing that the sequence consists of perfect squares allows us to quickly identify the next terms without having to perform complex calculations. This kind of pattern recognition is a fundamental skill in GCSE Maths and will help you solve various problems more efficiently.