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 Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion

 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: 21,026 Thanks: 2257 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. Tags arithmetic, geometric, progression ,
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Elementary Arithmetic and Geometric progression

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