What is an arithmetic progression
An arithmetic progression is one in which the difference between any 2 consecutive terms is a constant.
Examples of arithmetic progression
An arithmetic progression is one where the difference between ₙany 2 consecutive terms is a constant. This difference can be a positive or negative difference. Examples of arithmetic progressions are:
- 3, 5, 7, 9, 11, 13….. In this example here, the first term is 3, and to get to the next term, we add 2. We call 2 the common difference of this arithmetic progression.
- 20, 16, 12, 8, …… In this example here, the first term is 20, and to get to the next term, we add -4. We call -4 the common difference of this arithmetic progression.
General Expression for nth term and sum of first n terms
If a is the first term, and d is the common difference of an arithmetic progression,
nth term, uₙ = a+(n-1)d
sum of first n terms, Sₙ = ½n[2a+(n-1)d] = ½n[a +uₙ]
How to prove a sequence is an arithmetic progression?
Since an arithmetic progression is one where the difference between 2 consecutive terms is a constant, to prove an arithmetic progression, you’ll need to prove that uₙ – uₙ₋₁ = constant.
Sequences and series, AP& GP, and summation notes
- Sequences and series
- Arithmetic progression
- Geometric Progression
- Using the Graphic calculator (Ti84) for AP & GP Questions
- Summation: Introduction
- Finding summation using the graphic calculator
- Method of difference and summation
All the notes for H2 A Level Math
Go here to find all the notes and resources for H2 A level Math.