How to see it
Find the difference between terms. Here, it is 3 each time. That tells you the rule starts with 3n. Compare 3n to the sequence: 3, 6, 9, 12, and the sequence is 2 more every time. So the nth term is 3n plus 2. Now any term is a calculation.
A worked example
The hundredth term: 3 times 100 plus 2, 302. Which term is 49 in 3n plus 4? Set 3n plus 4 equal to 49, 3n equals 45, n equals 15.
The common mistake: using the difference alone as the rule
The trap is saying the rule is "add 3", or writing n plus 3. The nth term rule takes the position number n and gives the term. Check with n equals 1: it must give the first term.
Try one
Find the nth term of 7, 11, 15, 19.
- An + 4
- B4n + 3
- C3n + 4
- D4n
Show the answerHide the answer
Right: B, 4n + 3
The difference is 4, and 4n gives 4, 8, 12, so add 3.