in an infinite geomatric progression,each term is equal to 2 times the sum of the terms that follow.if the first term of the series is 8,find the sum of the series.
a)12 b)32/3
c)34/3 d)No any

• ans is 12.
  let 8=a/r,next term is a,next term ar and so on
  as per ques
  8=2(a+ar+ar2+ar3+...........infinity)
  8=2*a/1-r
  a/r=2*a/1-r
  r=1/3
  sum of infinite term of gp is
  1st term/1-r= 12
• 7 years agoHelpfull: Yes(9) No(2)
• Let the terms are ... a, ar, ar2, ar3,............infinity.
  as per ques,
  a=2(ar+ar2+ar3+...........infinity),
  =>a=2(a+ar+ar2+ar3+...........infinity - a),
  =>a=2(a/1-r) - 2a..............................bcz S(infinity)=(a/1-r),
  =>a=2a(r/1-r),
  =>1=2(r/1-r),
  =>r=1/3
  Therefore, sum of infinite term of GP is = a/1-r
  After putting value of a=8 and r=1/3,
  we get sum of infinite term of GP is = 12. Ans.
• 7 years agoHelpfull: Yes(6) No(0)
• For the geometric series, a+ar+ar2+... with |r|
• 7 years agoHelpfull: Yes(0) No(4)