How do I find the nth term of a sequence?

When given a sequence of numbers, there is often a rule using n, which symbolises the term of the sequence. For example in the sequence 3, 5, 7, 9, when n=1 it is referring to 3, since this is the first term of the sequence. To find this nth term rule, we first look for the difference between the consecutive terms. In this case, between each term is a difference of 2. This difference will be multiplied by the n, to start our rule. So the rule begins with 2n. To find the rest of the rule we choose a specific term to help us. When n=1 the nth term rule should produce 3. 2n in this case would be 2 x 1 = 2. We use addition and subtraction to reach the desired number, so we add 1 to 2 to get 3. As we added 1, the rule is 2n + 1. This is complete. The rule should work for any term within this sequence, so testing it will prove the answer is right. For example, when n = 2, 2n = 4. 2n+1= 5. This is correct as the second term of the sequence is 5. This has proven the nth term of the sequence to have correctly been found.