Transcription of Worksheet 3 6 Arithmetic and Geometric Progressions
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Worksheet 3 6 Arithmetic and Geometric Progressions
Worksheet3:6 ArithmeticandGeometricProgressionsSectio n1 ArithmeticProgressionAnarithmeticprogres sionis a listof numberswherethedi erencebetweensuccessive numbersis constant. Thetermsin an arithmeticprogressionareusuallydenotedas u1; u2; theinitialtermin theprogression,u2is thesecondterm,andso on;unis thenth anarithmeticprogressionis2;4;6;8;10;12;1 4; : : :Sincethedi erencebetweensuccessive termsis constant, we haveu3 u2=u2 u1andin generalun+1 un=u2 u1We willdenotethedi erenceu2 u1asd, which is a : Giventhat3,7and11arethe rstthreetermsin anarithmeticprogression,whatisd?
A geometric series is a geometric progression with plus signs between the terms instead of commas. So an example of a geometric series is 1+ 1 10 + 1 100 + 1 1000 + We can take the sum of the rst n terms of a geometric series and this is denoted by Sn: Sn = a(1 rn) 1 r Example 5 : Given the rst two terms of a geometric progression as 2 and 4, what
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