Arithmetic and geometric progressions
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The teaching part (1 min) is free to watch. A free account opens the whole lecture: 4 worked examples, 5 practice questions, 1 real past-paper question with the answer explained, the mistakes that lose marks, the full-marks tip, a one-card summary and a quick quiz.
What this lecture covers
- Two ways to grow
- Arithmetic progressions
Read the transcript of the teaching part
Last time
Before we start: last time, in Trigonometric equations and proving identities, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.
Two ways to grow
A savings plan adds the same amount each month. That is an arithmetic progression: add a fixed gap each time. A bouncing ball keeps a fixed fraction of its height each bounce. That is geometric: multiply by a fixed ratio. Both have neat formulas.
Arithmetic progressions
The nth term of an arithmetic progression is a plus n minus one, d. The sum of the first n terms is n over two, times twice a plus n minus one, d. Or n over two, times the first term plus the last term.
How often it comes up
How often Cambridge has asked each part, counted by ExamYard from every past paper in its question bank: Arithmetic and geometric progressions · Linked arithmetic and geometric progressions · Sum to infinity · Sums of an arithmetic progression.
The whole chapter: Series.
Chapter 1.6: Series
- Arithmetic and geometric progressions 5 min
- The binomial expansion 6 min
- Approximating with an expansion, progressions, and coefficients in progressions 6 min
- Linked progressions, progressions in context, trigonometric terms, and sums in a range 7 min
Also for A Level Maths 9709 Paper 1
Which topics come up most in A Level Maths 9709 Paper 1 past papers, counted from every paper since 2004.