6)Find the smallest number in a GP whose sum is 38 and product 1728

(a) 12
(b) 20
(c) 8
(d) none of these

• Sum of these numbers are:
  a/r +a +ar = 38
  a(1r+1+r) = 38 ---- (1)
  Product of these numbers are:
  a^3 = 1728
  = (12)^3
  a = 12
  
  Putting the value of a in (1) you will get:
  
  12(1r+1+r) = 38
  
  And factorising, we get
  r = 2/3 or r = 3/2
  
  Sub. the r and a value in (A), we get
  
  8,12,18 or 18,12,8. When a = 12
  
  And smallest no. is 8.
• 9 years agoHelpfull: Yes(5) No(0)
• 8
  8* 3/2=12
  12*3/2=18
  8+12+18=38
  8*12*18=1728
• 9 years agoHelpfull: Yes(4) No(0)