The first four terms of an arithmetic sequence are: 3, 10, 17, 24. What is an expression, in terms of n, for the nth term?

Before we start thinking about an expression for this sequence, we need to figure out what's going on. An arithmetic sequence means that there's a certain number being added on each time. By working out the difference between these numbers we can see that here the number being added is 7 (for example 10-3=7). So now we need to write our expression. This is just a way of showing someone what a sequence is without having to write it all out for them. It will be of the form d.n+a (try remembering it using DNA from science), where "d" and "a" are what you need to find out. The first one is easy: "d" stands for difference and we've already worked out that is 7.To work out "a", siimply substract the difference, 7, from the first number in the sequence (called the first "term"), which is 3. 3-7=-4, so "a" is -4.You can conclude that the expression is 7n-4.