Maths · Algebra and graphs. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
A sequence is a list of numbers that follows a rule. The term-to-term rule tells you how to get from one term to the next, for example "add 4" or "multiply by 3".
The nth term is a formula that gives any term from its position n. Put n = 1 for the first term, n = 2 for the second, and so on.
To find the rule, write down the differences between terms. If the first differences are the same, the sequence is linear. If the second differences are the same, it is quadratic and contains n2. If each term is multiplied by the same number, it is geometric. Also compare the terms with the square numbers and cube numbers.
For 7, 11, 15, … many students write n + 4 because the terms go up by 4. The difference multiplies n, so the nth term is 4n + 3. Always test your formula with n = 1 and n = 2.
Answer: nth term = 2n² + n
Type what you are stuck on. The helper finds the explanation, worked examples and the notes to read, free and instant.