Find an expression for the nth term of the following sequence: 7, 11, 15, 19

In terms of understanding the question, we are asked to look for a common rule that would help us find any term, or member, of the sequence in the question, no matter how big. The "nth" bit they talk about is just a way of describing which term we are talking about: for example, in this sequence 7 is the 1st "term" and so for 7, n=1. This pattern continues with 11 being n=2, 15 being n=3 and so on. To find an unifying rule we need to find the difference between each of the terms and see if there is a pattern. As we can see the terms are separated by the number 4; 11-7 is 4, 15-11 is 4 and 19-15 is 4. So the first thing we know is that the number of n must be multiplied by 4. So to start the expression we have 4n. Now if we look back at what this gives us, the first 4 terms of our sequence would look like this: 4, 8, 12, 16. As we can see, this isn't quite what the question was looking for. However we are very close and if you look at the difference between the sequence we have and the sequence in the question we can see that each of our terms is exactly 3 smaller. Therefore we can complete our expression by adding 3 at every step. So we can present our final answer with the expression being 4n+3.