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# Series watch

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1. The sum to infinity of a geometric series is 5 and the first term is 2.
Find the common ratio of the series..

and The first 3 terms of an arithmetical progression are 7, 5.9 and 4.8

Find
i)the common difference
ii)the smallest value of n for which the sum to n terms is negative
2. 2/(1 - r) = 5
1 - r = 2/5
r = 3/5

--

d = 5.9 - 7 = -1.1

S(n)
= sum of first n terms
= (1/2)n[first term + nth term]
= (1/2)n[7 + (7 - 1.1(n - 1))]
= (1/2)n[14 - 1.1(n - 1)]

S(n) is negative when

14 - 1.1(n - 1) < 0
(n - 1) > 14/1.1
n > 14/1.1 + 1

Smallest such value of n = 14

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Updated: January 5, 2005
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