The sum of the term of an infinite G.P. is 9/4.The sum of the squares of the terms of the series is 81/80.Find the second term of the series.

• sum of an infinite gp is a/1-r and series is a,ar,ar2,ar3.....infinite.
  and sum of square of this series is --- a2/1-r2
  since a/1-r=9/4 and a2/1-r2=81
  a=9/4(1-r) put into second eqn n get r=2/3 n a=3/4 and second term =ar= 1/2
• 9 years agoHelpfull: Yes(35) No(3)
• answer will be 1/2. when we solve both the equations, 4a=9-9r, 80a^2=81-81^2.
  we get a=3/4 and r=2/3. so. ar=1/2.
• 9 years agoHelpfull: Yes(3) No(0)
• sum of infinite g.p=a/1-r........(1)
  so,9/4=a/1-r
  and 81/80=a^2/1-r^2................(2)
  from eqn (1) and (2)
  we get a=3 and r=-1/3
  so 2nd term=ar=-1
  so ans is -1
• 9 years agoHelpfull: Yes(1) No(5)
• 1/2 ans
  a/1-r = 9/4
  a^2/(1-r^2) = 81/80
  On solving these r = 2/3
  a=3/4
  2nd term =ar = 1/2
• 9 years agoHelpfull: Yes(1) No(0)
• sum of an infinite gp is a/1-r and series is a,ar,ar2,ar3.....infinite.
  and sum of square of this series is --- a2/1-r2
  since a/1-r=9/4 and a2/1-r2=81/80
  a=9/4(1-r) put into second eqn n get r=2/3 n a=3/4 and second term =ar= 1/2
• 9 years agoHelpfull: Yes(1) No(0)