What is the pattern in the sequence 5, 11, 17, 23?

The pattern in the sequence 5, 11, 17, 23 is that each term increases by 6 from the previous term.

To analyse this sequence in more detail, let's look at the differences between each consecutive term. Starting with the first term, 5, and moving to the second term, 11, we can see that 11 - 5 = 6. Similarly, for the next pair of terms, 17 - 11 = 6, and for the final pair given, 23 - 17 = 6. This consistent difference of 6 indicates that the sequence is an arithmetic sequence, where each term is obtained by adding a fixed number, known as the common difference, to the previous term.

In an arithmetic sequence, the nth term can be found using the formula: \( a_n = a_1 + (n - 1)d \), where \( a_n \) is the nth term, \( a_1 \) is the first term, \( n \) is the term number, and \( d \) is the common difference. For this sequence, the first term \( a_1 \) is 5, and the common difference \( d \) is 6. So, the nth term formula for this sequence is \( a_n = 5 + (n - 1) \times 6 \).

For example, to find the 4th term, substitute \( n = 4 \) into the formula: \( a_4 = 5 + (4 - 1) \times 6 = 5 + 18 = 23 \). This matches the given sequence, confirming our pattern. Understanding this pattern helps in predicting future terms and solving related problems in GCSE Maths.