SEQUENCES AND SERIES

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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.

9.2 Sequences Let us consider the following examples: Assume that there is a generation gap of 30 years, we are asked to find the number of ancestors, i.e., parents, grandparents, great grandparents, etc. that a person might have over 300 years. Here, the total number of generations = 300 10 30 = Fibonacci (1175-1250) Chapter SEQUENCES AND SERIES 9

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