Discrete structure lecture_18

Apr 28th, 2015
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It includes all the details about the Discrete structure with examples.Step by step solution.

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DISCREAT STRUCTURELECTURE # 18GEOMETRIC SERIESKHAWAJA TARIQ MAHMOODLecture # 18GEOMETRIC SERIESGEOMETRIC SERIES:A sequence of numbers in which every term after the first is obtained from thepreceding term by multiplying it with a constant number, is called common ratio. In other words,a geometric progression is a sequence of numbers in which the same quotient is obtained bydividing any term after the first by the preceding term. This quotient is called the common ratio.THE nth TERM OF A GEOMETRIC SERIES:Let the common ratio be denoted by r, the first term by a1, the nth term by an and thenumber of terms by n. The nth term of the geometric progression isan a1r n1EXAMPLE:Find the 9th, 10th and 11th term of the G.S. 2, 1,1, .2SOLUTION:a1 212a9 ?ra10 ?a11 ?9th terman a1r n11a9 2 29 11a10 2 281a10 2 22a10 921a10 9121a9 2 2a9 a9 10th terman a1r n12281281Khawaja Tariq Mahmood.11th terman a1r n110 11a11 2 211191a11 2 22a11 1021a11 101210Page 2Lecture # 18GEOMETRIC SERIESa9 a9 127a10 1128128a10 a11 1256129a11 1512SUM OF THE n TERMS OF A GEOMETRIC SERIES:a1 (r n 1)Sn r 1a1 (1 r

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