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 January 16th, 2017, 04:45 AM #1 Member   Joined: Sep 2016 From: zambia Posts: 31 Thanks: 0 Arithmetic and Geometric progression An arithmetic series has first term -4 and common diffrence of 1.A geometric series has a first term of 8 and a common ratio of 0.5.After how many terms does the sum of the arithmetic series exceed the sum of the geometric series?
January 16th, 2017, 06:20 AM   #2
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Quote:
 Originally Posted by jeho An arithmetic series has first term -4 and common diffrence of 1. A geometric series has a first term of 8 and a common ratio of 0.5. After how many terms does the sum of the arithmetic series exceed the sum of the geometric series?
$\dfrac{n}{2}[-8 + (n-1)] > \dfrac{8(1-0.5^n)}{1-0.5}$

$\dfrac{n}{2}(n-9) > 16(1-0.5^n)$

my calculator sez when $n = 12$ terms ...

January 18th, 2017, 04:04 AM   #3
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Quote:
 Originally Posted by jeho An arithmetic series has first term -4 and common diffrence of 1.A geometric series has a first term of 8 and a common ratio of 0.5.After how many terms does the sum of the arithmetic series exceed the sum of the geometric series?
So the first series is -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17 ...
and the second series is 8, 12, 14, 15, 15 1/2,15 3/4, 15 7/8, ...

Looks like basic arithmetic to me.

 January 18th, 2017, 05:25 AM #4 Global Moderator   Joined: Dec 2006 Posts: 20,746 Thanks: 2133 The question's wording is ambiguous. It isn't clear whether each series is summed to the same number of terms, and it isn't clear what "after" means.

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