f(x+y)= f(x)*f(y); f(x)=1.6, f(1)+f(2)+f(3)+.........f(n) lies between 24 and 32 then what is the value of n.

• Firstly its f(1)=1.6
  here it is given that f(x+y)=f(x)*f(y)
  f(1)=1.6
  f(2)=f(1)*f(1)=1.6*1.6
  f(3)=f(2)*f(1)=1.6*1.6*1.6
  similarly for f(4) = 1.6 ^ 4
  thus forming the gp
  sum of gp to n terms is (a(r^n-1))/(r-1)
  here a=1.6 and r=1.6
  (1.6((1.6)^n - 1))/(1.6 - 1) => 2.67((1.6)^n - 1) = for n=5 the value comng is 25.32 ,, thus the value of n=5
• 9 years agoHelpfull: Yes(20) No(3)
• f(x)=1.6
  f(x-1+1)=1.6 =>f(x-1+1)=f(x-1)*f(1)=1.6
  now let f(x-1)=.8 and f(1)=2
  so
  f(1)=2
  so f(2)=f(2-1+1)=f(2-1)*f(1)=f(1)*f(1)
  so
  f(2)=f(1)*f(1)=2*2=4
  so f(3)=f(2)*f(1)=4*2=8
  f(4)=f(3)*f(1)=8*2=16
  now 2+4+8+16=30 lies in24 t0 32
  so n=4
• 9 years agoHelpfull: Yes(5) No(1)
• Given: - f(x+y)=f(x)*f(y) ___________(1) and 24
• 9 years agoHelpfull: Yes(2) No(0)