10B-Geometric Series - Geometric Series The sum of the terms in a geometric progression is called a geometric series For the geometric progression cfw_a

# 10B-Geometric Series - Geometric Series The sum of the...

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1 Geometric Series The sum of the terms in a geometric progression is called a geometric series. For the geometric progression {a, ar, ar2, ar3, . . . } the corresponding geometric series would be: a + ar + ar2+ ar3+ . . . Let Snrepresent the sum of ‘n’ terms of a geometric series: Sn= a+ a r+ a r2+ a r3+ .....+ a rn-2 + Sn×r= (a+ a r+ a r2+ a r3+ .....+ a rn-2 + a rn-1) ×r= a r+ a r2+ a r3+ .....+ a rThe difference between Sn×r and Snis then: (Sn×r) – Sn= a r+ a r2+ a r3+ .....+ a rn-1 + a rn– (a+ a r+ a r2+ a r3+ .....+ a rn-2 (Sn×r) – Sn= a rnSn (r– 1) = a (rnn(1)S(1)na rr-=-Example 1: Find the sum of the geometric series given by: 3, 9, 27, . . . . . 729. Example 2: Find the sum of the geometric series given by: 3, 1, 1/3, . . . . . 1/81. a r n-1 n-1 + a r n + a r n-1 ) a 1 )
2 Exercises: 1.Find the sum of the first ten terms of the geometric series given by: 1, 2, 4, . . . 2.Find the sum of the first six terms of the geometric series given by: 1/3, 1/9, 1/27. . . 3.Find the sum of the first five terms of the geometric series given by: 1, -1/2, 1/4, -1/8, . . . 4.A car was purchased in 2001 for \$10000. It depreciated at 20% per year.