find the four numbers in G.P. in which third term is greater than first by 9, second term is greater than foutht by 18 ? 

Dear Raju

let the numbers are a, ar, ar², ar³

from the given conditions

ar²-a=9   ........(1)

ar-ar³=18   ......(2)

dividing (2) by (1)

(r-r³)/(r²-1)=18/9

r(1-r²)/(r²-1)=2

r= -2

putting r=-2 in (1)

a=3

hence numbers will be 3,-6,12,-24

All the best.

AKASH GOYAL

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let the numbers are   a/r  ,  a  ,ar  , ar² 

third term is greater than first by 9 so

ar=a/r +9 or  ar² =a+9r...........1

also second term is greater than fourth by 18 so

a =ar² +18.......2

solving 1 and 2 we get r=-2 & a=-6

therefore numbers are  3 , -6 ,12 ,-24