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?7 3 = 11 7 = 4 Thend= 4. Thatis, thecommondi erencebetweenthetermsis we know the rsttermin anarithmeticprogression, andthedi erencebetweenterms,thenwe canworkoutthenth term, canworkoutwhatany termwillbe. Theformulawhichtellsus whatthenth termin anarithmeticprogressionisun=a+ (n 1) dwhereais the : If the rst3 termsin anarithmeticprogressionare3,7,11thenwhat is the10thterm?
worksheet 3.7. The condition that S1 exists is that r is greater than 1 but less than 1, i.e. jrj < 1. If this is the case, then we can use the formula for Sn above and let n grow arbitrarily big so that rn becomes as close as we like to zero. Then S1 = a 1 r
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