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 October 2nd, 2019, 09:47 AM #1 Newbie   Joined: Oct 2019 From: San diego Posts: 3 Thanks: 0 Geometric sequence How can I find x so that a+x, b+x, c+x is a geometric sequence? Last edited by skipjack; October 2nd, 2019 at 07:52 PM. October 2nd, 2019, 10:05 AM #2 Global Moderator   Joined: Dec 2006 Posts: 21,035 Thanks: 2271 You need (a + x)(c + x) = (b + x)². Thanks from idontknow October 2nd, 2019, 10:17 AM #3 Senior Member   Joined: Dec 2015 From: somewhere Posts: 734 Thanks: 98 Now just set a,b,c the way you want and find their values. Note: If (p,q,r) is a geometric sequence, (r,q,p) is also a geometric sequence. Last edited by skipjack; October 2nd, 2019 at 07:51 PM. October 2nd, 2019, 04:37 PM   #4
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Found a solution

Quote:
 Originally Posted by skipjack You need (a + x)(c + x) = (b + x)².
Geometric Sequence – Math tutor in San Diego October 2nd, 2019, 04:38 PM   #5
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Funny but true

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 Originally Posted by idontknow Now just set a,b,c the way you want and find their values . Note: If {p,q,r} is a geometric sequence then {r,q,p} is also a geometric sequence .
You're actually correct

1,3,9 and 9,3,1 are both geometric sequences.
First one has a ratio of 3, the second one has a ratio of 1/3 October 2nd, 2019, 07:54 PM #6 Global Moderator   Joined: Dec 2006 Posts: 21,035 Thanks: 2271 What if no such x exists? October 3rd, 2019, 02:54 AM #7 Senior Member   Joined: Feb 2010 Posts: 714 Thanks: 151 I think that will happen if $\displaystyle b$ is the arithmetic mean of $\displaystyle a$ and $\displaystyle c$. Thanks from idontknow October 3rd, 2019, 03:01 AM   #8
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Quote:
 Originally Posted by mrtwhs I think that will happen if $\displaystyle b$ is the arithmetic mean of $\displaystyle a$ and $\displaystyle c$.
for x=1 : {1+a,1+b,1+c}. Now set a=1,b=3,c=7 and we have a geometric sequence {2,4,8} where the ratio is $\displaystyle q=2$.
Also {8,4,2} where the ratio is $\displaystyle q=1/2$. Tags geometric, sequence Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Tomedb Algebra 1 November 3rd, 2016 03:17 PM med1student Algebra 3 March 5th, 2016 08:48 AM frukoprof Computer Science 25 May 9th, 2013 07:35 PM Vince604 Algebra 6 November 15th, 2012 08:39 PM emohbe Algebra 3 December 13th, 2010 10:00 PM

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