DISCREAT STRUCTURE LECTURE # 18 GEOMETRIC SERIES KHAWAJA TARIQ MAHMOOD Lecture # 18 GEOMETRIC SERIES GEOMETRIC SERIES: A sequence of numbers in which every term after the first is obtained from the preceding 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 by dividing 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 the number of terms by n. The nth term of the geometric progression is an  a1r n1 EXAMPLE: Find the 9th, 10th and 11th term of the G.S. 2, 1, 1 , ………. 2 SOLUTION: a1  2 1 2 a9  ? r a10  ? a11  ? 9th term an  a1r n1 1 a9  2   2 9 1 1 a10  2   2 8 1 a10  2   2 2 a10  9 2 1 a10  91 2 1 a9  2   2 a9  a9  10th term an  a1r n1 2 28 1 281 Khawaja Tariq Mahmood. 11th term an  a1r n1 10 1 1 a11  2   2 111 9 1 a11  2   2 2 a11  10 2 1 a11  101 2 10 Page 2 Lecture # 18 GEOMETRIC SERIES a9  a9  1 27 a10  1 128 1 28 a10  a11  1 256 1 29 a11  1 512 SUM OF THE n TERMS OF A GEOMETRIC SERIES: a1 (r n  1) Sn  r 1 a1 (1  r ...
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