Transcription of SEQUENCES AND SERIES
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SEQUENCES AND SERIES
VNatural numbers are the product of human spirit. DEDEKIND mathematics, the word, sequence is used in much thesame way as it is in ordinary English. When we say that acollection of objects is listed in a sequence , we usually meanthat the collection is ordered in such a way that it has anidentified first member, second member, third member andso on. For example, population of human beings or bacteriaat different times form a sequence . The amount of moneydeposited in a bank, over a number of years form a values of certain commodity occur in asequence. SEQUENCES have important applications in severalspheres of human , following specific patterns are called progressions. In previous class,we have studied about arithmetic progression ( ). In this chapter , besides discussingmore about ; arithmetic mean, geometric mean, relationship between , special SERIES in forms of sum to n terms of consecutive natural numbers,sum to n terms of squares of natural numbers and sum to n terms of cubes ofnatural numbers will also be SequencesLet us consider the following examples:Assume that there is a generation gap of 30 years, we are asked to find thenumber of ancestors, , parents, grandparents, great grandparents, etc.
Chapter SEQUENCES AND SERIES 9 178 MATHEMATICS The number of person’ s ancestors for the first, second, third, …, tenth generations are 2, 4, 8, 16, 32, …, 1024. These numbers form what we call a sequence. Consider the successive quotients that we …
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