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Subject: "Geometric series ratios"     Previous Topic | Next Topic
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Conferences The CTK Exchange High school Topic #380
Reading Topic #380
ke_45
guest
Jun-17-08, 10:59 AM (EST)
 
"Geometric series ratios"
 
   We have an arithmetic progression the squares of whose 12h, 13th, and 15th terms form a geometric progression. Find all the ratios of this progression.

Assuming

u_n+1 = u_n + d -or- u_n+1 = u_1 + d*n

for the arithmetic progression, and

u_n+1 = u_n * q -or- u_n+1 = u_1 * q^(n-1)

for the geometric one, how do we go about this? (My results don't match with the answer in the book I took this from.)

Please only hint, don't solve!


Thanks
-- KE


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alexbadmin
Charter Member
2236 posts
Jun-17-08, 11:02 AM (EST)
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1. "RE: Geometric series ratios"
In response to message #0
 
   If the initial arithmetic progrssion is a +i·d, then the condition is

(a + 15d)² / (a + 13d)² = (a + 13d)² / (a + 12d)²

which gives you

(a + 15d)² · (a + 11d)² = (a + 13d)² · (a + 13d)².

There are two ways to get rid of the square. Try both.


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