What is the pattern in the sequence 5, 10, 15, 20?

The pattern in the sequence 5, 10, 15, 20 is that each number increases by 5.

This sequence is an example of an arithmetic sequence, where the difference between consecutive terms is constant. In this case, the common difference is 5. To find the next term in the sequence, you simply add 5 to the previous term. For instance, starting with 5, you add 5 to get 10, then add another 5 to get 15, and so on.

Arithmetic sequences are a fundamental concept in GCSE Maths, and they help you understand how numbers can progress in a predictable manner. The general formula for the nth term of an arithmetic sequence is given by \( a_n = a + (n-1)d \), where \( a \) is the first term, \( d \) is the common difference, and \( n \) is the term number. For this sequence, \( a = 5 \) and \( d = 5 \), so the nth term can be calculated as \( a_n = 5 + (n-1) \times 5 \).

Understanding this pattern is useful not only in solving problems related to sequences but also in real-life situations where regular intervals or increments are involved, such as saving money, planning schedules, or even in certain scientific measurements. By recognising and working with arithmetic sequences, you can develop a stronger grasp of how numbers and patterns work together in mathematics.