Sequences and Series

What the page covers

The unit begins with patterns and ends with convergence. Early resources deal with number patterns, the Fibonacci sequence, triangular numbers and finding the nth term. Further along you meet arithmetic and geometric progressions, sigma notation, the method of differences, recurrence relations and sum to infinity. Some university-level flashcards go on to the ratio test, power series and Maclaurin series.

Where to start

If sequences are new to you, begin with the flashcards on Sequences (nth term). They ask you to find the nth term of lists such as 1, 5, 9, 13, 17. Then read the note The nth Term, which explains position-to-term rules with a simple table. The note Nth term rule adds the difference between a term-to-term rule and an nth term rule.

Next, move on in this order:

1. Work through Quadratic Sequences, where a constant second difference is the key idea.
2. Learn the formulas in Arithmetic Sequences and Series.
3. Practise sums and geometric means with Sequences + Series + Means 10.
4. Look at the slides on geometric series and sum to infinity.

Using quizzes and maps together

Open a mind map first to see how the ideas connect. There are several on arithmetic progression, Fibonacci and summing sequences. Then take a quiz such as Geometric Sequence or Have fun with arithmetic and geometric sequences. Note which questions slow you down, go back to the matching map or flashcard deck, and try the quiz again later.

Where it sits

This unit belongs to the Algebra strand of Mathematics. The listed resources mention GCSE Maths, A-level Mathematics, A-level Maths, IB and CBSE Class 10, so most of the material suits secondary study, with a smaller share aimed at university.

Make it your own

Choose one resource that matches what you are studying today, work through it, and then build a map or flashcard set of your own for the formulas you keep forgetting.