G1,G2,G3,G4 are in G.P, where G=G1 and R is the common ration and log4(G1)+log4 G2 +log4 G3 +.... = 2500, then find the possible pair of (G,R).

• G1,G2,G3,G4 are in G.P
  G1=G, G2=G*R , G3=G*R^2 , G4=G*R^3
  
  log4(G1)+ log4 G2 +log4 G3 +log4 G4 = 2500
  => log4(G1*G2*G3*G4)=2500
  => G1*G2*G3*G4 = 4^2500
  => G*GR*GR^2*GR^3= 4^2500
  => G^4*R^6= 4^2500
  => G^2*R^3= 2^2500
  
  (G,R)=[ 2^1250/R^(3/2) , R]
  
  IF R=1, G^2=2^2500 => G=2^1250
  IF R=2^2, G^2=2^2494 => G=2^1247
  IF R=2^4, G^2=2^2488 => G=2^1244
  and so on........
• 10 years agoHelpfull: Yes(13) No(6)
• how is it possible
  (G,R)=[ 2^1250/R^(3/2) , R]
  IF R=1, G^2=2^2500 => G=2^1250
  IF R=2^2, G^2=2^2494 => G=2^1247
  IF R=2^4, G^2=2^2488 => G=2^1244
  and so on........
• 10 years agoHelpfull: Yes(2) No(0)
• Rakesh's solution is right till the expression (G,R)=[ 2^1250/R^(3/2) , R]. He wend wrong on his assumptions thereafter. We could get the answer by putting all values in the options for R and finding G.
• 10 years agoHelpfull: Yes(0) No(1)
• provide a valid solution
• 10 years agoHelpfull: Yes(0) No(1)
• are there only 4 terms in series or is it upto n Terms if just 4 terms then G=4^622
  R=4^2
• 10 years agoHelpfull: Yes(0) No(0)
• R =G=4^250
  
• 10 years agoHelpfull: Yes(0) No(1)
• Given G1,G2,G3,G4 are in G.P.
  Let G1=G,G2=GR,G3=G(R)^2,G4=G(R)^3
  
  Log(G1)base4+.........................+Log(G4)base4=2500
  
  Log(G1G2G3G4)=2500 putting values of G1,G2,G3,G4
  (G^4) (R^6)=42500
  (G,R)=[(2^1250)/(R^(2/3)) ,R]
• 7 years agoHelpfull: Yes(0) No(0)