I struggle with the following type of question: "The first four terms of an arithmetic sequence are 5, 9, 13, 17. Write down an expression, in terms of n, for the nth term in the sequence." How should I approach this?

The way I would suggest approaching a question like this is to imagine n=1, n=2, n=3 and n=4 above the terms given, or even to literally write that above each of the 4 given numbers. n ---------- 1 2 3 4result----- 5 9 13 17The key is to understand that the same arithmetic (multiplying and adding) formula describes each pair (2 and 9 is a pair, 4 and 17 is another pair) here. Furthermore, it is key to look at what changes each time between the result. Here we can see that each result is 4 greater than the last. This means that, as n increases by 1, the result increases by 4. This means that there must be a 4n term in the formula for the sequence. So if we apply that, we get the result: 4, 8, 12, 16. This is clearly 1 out for each result, so we can deduce that the formula really is:nth term = 4n + 1.