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The sum of an infinite geometric progression is 6 . If the sum of the first two terms is 9 / 2 , then what is the first term?

Options

  1. A1
  2. B5 / 2
  3. C3 or 3 / 2
  4. D9 or 3

Correct answer

D. 9 or 3

Step-by-step solution

Given a+a r= 9 2 a(1+r)= 9 2 ...(i) array rlrl Again 6 & = a 1-r & a & =6(1-r)...(ii) array aligned & from (i) 6 (1-r^2 )= 9 2 & aligned -12 r^2 & =-3 r & = 1 2 a & =6 (1- 1 2 )=3 or 6 (1+ 1 2 )=9 a & =9 or 3 . aligned aligned

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