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# Arithmetic Progression (AP)

## 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.

## All the notes for H2 A Level Math

Go here to find all the notes and resources for H2 A level Math.

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