# 31: Arithmetic Sequences and Series © Christine Crisp “Teach A Level Maths” Vol. 1: AS Core Modules

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• Module C1AQAEdexcelOCRMEI/OCRModule C2"Certain images and/or photos on this presentation are the copyrighted property of JupiterImages and are being used with permission under license. These images and/or photos may not be copied or downloaded without permission from JupiterImages"

• d = 2nd term 1st term= 3rd term 2nd term . . . = 2Arithmetic Sequence

• Arithmetic SequenceAn arithmetic sequence is of the formNotice that the 4th term has 3d added so, for example, the 20th term will beAn arithmetic sequence is sometimes called an Arithmetic Progression (A.P.)

• Arithmetic SeriesWhen the terms of a sequence are added we get a seriesThe Sum of an Arithmetic SeriesWe can derive a formula that can be used for finding the sum of the terms of an arithmetic series

• Arithmetic SeriesAdding the 1st and last terms gives 11. Adding the 2nd and next to last terms gives 11. The 10 terms give 5 pairs of size 11 ( = 55 ).Writing this as a formula we have where l is the last term

• With an odd number of terms, we cant pair up all the terms. e.g.Arithmetic Seriesgiving n = 6. Now we add the middle term

• However, still works since we can miss out the middle termWith an odd number of terms, we cant pair up all the terms. e.g.Arithmetic Seriesgiving n = 6. Now we add the middle term

• For any arithmetic series, the sum of n terms is given by Substituting for l in the formula for the sum gives an alternative form:Since the last term is also the nth term,

• SUMMARYThe sum of n terms of an arithmetic series is given byAn arithmetic sequence is of the formThe nth term is or

• e.g.1Find the 20th term and the sum of 20 terms of the series:2 + 5 + 8 + 11 + 14 + 17 + . . . Solution: The series is arithmetic.

• e.g.2The common difference of an arithmetic series is -3 and the sum of the first 30 terms is 255. Find the 1st term. Solution:

• Exercises2.Find the sum of the series given byWe can see the series is arithmetic so,Substituting n = 1, 2 and 3, we get -6, -2, 2

• The following slides contain repeats of information on earlier slides, shown without colour, so that they can be printed and photocopied.For most purposes the slides can be printed as Handouts with up to 6 slides per sheet.

Arithmetic Sequences and Series

Arithmetic Sequences and Series

Arithmetic Sequences and Series

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