As we know that, single GM between two numbers a and b will be +(root (a*b)), Could anybody tell me, why not -- (root (a*b)) While, 4 8 16 and 4 -8 16 both are in GP.

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There are two parts to your question. 1. Can a GM be negative. 2. Does the calculation follow from this formula which you have stated. Answer to the first part is yes. GM can be negative. Answer to the second part is no. We don't directly use the formula which you have used. We have to do something...
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There are two parts to your question. 1. Can a GM be negative. 2. Does the calculation follow from this formula which you have stated. Answer to the first part is yes. GM can be negative. Answer to the second part is no. We don't directly use the formula which you have used. We have to do something called as normalization. A good example of negative GM comes in investment sector. http://www.investopedia.com/ask/answers/06/geometricmean.asp. Check this site. for a better insight read less
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we already replayed for this question Kindly check once
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Math tutor with 25 plus years experience.

4, -8, 16 are not in GP.
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Chemistry Wizard/English Expert

http://www.jagranjosh.com/articles/arithmetic-progression-ap-geometric-gp-and-harmonic-progression-hp-cat-quantitative-aptitude-1337821417-1
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Because AM as well GM between two numbers a and b lie between them and -8 does not lie between a and b
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20 years of experience as Maths Tutor

4 -8 16 forms a GP with common ratio -2
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In GP, series should be always in with common ratio. 4 , -8 , 16 cannot be in GP. GM will be always +( root (a*b))
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whenever we ask for a GM then we didn't consider Alternating series
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i am a faculty of business studies subject.
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Hi bhaskar, G.M only applies to positive numbers.if u see the g.m of 4,8,16 its cuberoot of the three numbers.so if u take any one of these no.s as negative how can u take out the cube root.that will then give you an imaginary value.also u have written --(root(a*b).while if u write -8 as one of the...
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Hi bhaskar, G.M only applies to positive numbers.if u see the g.m of 4,8,16 its cuberoot of the three numbers.so if u take any one of these no.s as negative how can u take out the cube root.that will then give you an imaginary value.also u have written --(root(a*b).while if u write -8 as one of the number u need to put b=-8.i hope that explains.if any doubts please ask. read less
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