What is the next term in the sequence 1, 3, 5, 7?

The next term in the sequence 1, 3, 5, 7 is 9.

This sequence is an example of an arithmetic sequence, where each term increases by a constant amount. In this case, the common difference between each term is 2. To find the next term, you simply add this common difference to the last term in the sequence. So, starting with 1, you add 2 to get 3, then add 2 again to get 5, and so on. When you add 2 to 7, you get 9.

Arithmetic sequences are a fundamental concept in GCSE Maths. They are sequences of numbers where the difference between consecutive terms is always the same. This difference is known as the common difference. In our sequence, the common difference is 2, which means each term is 2 more than the previous one. Understanding how to identify and extend arithmetic sequences is important because it helps you recognise patterns and solve problems more easily.

To generalise, if you know the first term (a) and the common difference (d) of an arithmetic sequence, you can find any term in the sequence using the formula: \( a_n = a + (n-1)d \), where \( a_n \) is the nth term. For our sequence, the first term \( a \) is 1, and the common difference \( d \) is 2. So, the nth term can be found using \( a_n = 1 + (n-1) \times 2 \). For the 5th term, \( a_5 = 1 + (5-1) \times 2 = 1 + 8 = 9 \).