How can I find x so that a+x, b+x, c+x is a geometric sequence?

J JohnSecada2019 Oct 2019 3 0 San diego Oct 2, 2019 #1 How can I find x so that a+x, b+x, c+x is a geometric sequence? Last edited by a moderator: Oct 2, 2019

skipjack Forum Staff Dec 2006 21,482 2,472 Oct 2, 2019 #2 You need (a + x)(c + x) = (b + x)Â². Reactions: 1 person

idontknow Dec 2015 1,085 169 Earth Oct 2, 2019 #3 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 a moderator: Oct 2, 2019

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.

J JohnSecada2019 Oct 2019 3 0 San diego Oct 2, 2019 #4 Found a solution skipjack said: You need (a + x)(c + x) = (b + x)Â². Click to expand... Geometric Sequence â€“ Math tutor in San Diego

Found a solution skipjack said: You need (a + x)(c + x) = (b + x)Â². Click to expand... Geometric Sequence â€“ Math tutor in San Diego

J JohnSecada2019 Oct 2019 3 0 San diego Oct 2, 2019 #5 Funny but true idontknow said: 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 . Click to expand... 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

Funny but true idontknow said: 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 . Click to expand... 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

mrtwhs Feb 2010 739 162 Oct 3, 2019 #7 I think that will happen if \(\displaystyle b\) is the arithmetic mean of \(\displaystyle a\) and \(\displaystyle c\). Reactions: 1 person

I think that will happen if \(\displaystyle b\) is the arithmetic mean of \(\displaystyle a\) and \(\displaystyle c\).

idontknow Dec 2015 1,085 169 Earth Oct 3, 2019 #8 mrtwhs said: I think that will happen if \(\displaystyle b\) is the arithmetic mean of \(\displaystyle a\) and \(\displaystyle c\). Click to expand... 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 \(\displaystyle q=1/2\).

mrtwhs said: I think that will happen if \(\displaystyle b\) is the arithmetic mean of \(\displaystyle a\) and \(\displaystyle c\). Click to expand... 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 \(\displaystyle q=1/2\).