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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... read more
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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Math tutor with 25 plus years experience.

4, -8, 16 are not in GP.
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Coaching for all students

whenever we ask for a GM then we didn't consider Alternating series
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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... read more
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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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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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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B.E. in Electronics and Communication and MBA in Finance

very good question Bhaskar. The formula to calculate GM you mentioned above is only valid if both numbers are positive. There is a different way to calculate GM for numbers some negetive numbers as well as with zero. For class 12th std, GM calculation for the above mentioned method will be too complex... read more
very good question Bhaskar. The formula to calculate GM you mentioned above is only valid if both numbers are positive. There is a different way to calculate GM for numbers some negetive numbers as well as with zero. For class 12th std, GM calculation for the above mentioned method will be too complex for you as it also requires application of functions in logarithms and solution method depends upon the number of variables you are looking at. (Different method for even and odd). I hope that solves you inquisitiveness. If you want to learn more about those methods you can write me a mail read less
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i am a faculty of business studies subject.
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4 -8 16 forms a GP with common ratio -2
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