Three numbers are in A.P., and the product of them is same as product of smallest and largest. What
is the middle number?
a) 1 b) -1 c) 2 d) -2

• let 3 A.P terms are a,a+d,a+2d
  a is the 1st no.
  a+d is the middle one and
  a+2d is the last no.
  According to question a*(a+d)*(a+2d)=a*(a+2d)
  => a+d=1
  Therefore middle no.is 1
• 9 years agoHelpfull: Yes(16) No(0)
• let x,y,z are 3 members in ap
  they given product of xyz=product of xz
  if we subbstitute y=1 in xyz product then we will get it as xz
  so y=1
• 9 years agoHelpfull: Yes(1) No(0)
• ans = a(1)
  since;
  the A.P is-> -1,1,3 so the prdct of them is -3 and the prdct of -1 & 3 is -3.
  so the middle term is 1.
• 9 years agoHelpfull: Yes(0) No(1)
• assume a,b,c in a.p then given abc=ac so b=1
• 9 years agoHelpfull: Yes(0) No(0)
• (a-d)*a*(a+d)=(a-d)*(a+d)
  0r,a=1
• 9 years agoHelpfull: Yes(0) No(0)
• let us assume three values which are in a.p
  x,x+1,x+2
  as given in the question product of these three values=product of small and largest
  i.e x*x+1*x+2=x*x+2
  x(x^2+3x+2)=x(x+2)
  x(x+2)=0;
  x=-2 or 0
  if u consider 0 the middle value is 1
  if u consider -2 the middle value is -1
• 9 years agoHelpfull: Yes(0) No(0)
• Middle term is 1
  suppose all the 3 terms are a-x, a, a+x
  so product of the three = product of smallest and largest
  therefore (a-x)*a*(a+x)=(a-x)*(a+x)
  therefor a=(a-x)*(a+x)/(a-x)*(a+x) =1
  
• 9 years agoHelpfull: Yes(0) No(0)
• let the 3 nos in AP be a-d,a,a+d
  ATQ
  (a-d)(a)(a+d)=(a-d)(a+d)
  => a(a^2-d^2)=a^2-d^2) =>a=1
  hence ans is a)1
• 9 years agoHelpfull: Yes(0) No(0)