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A geometric progression (GP) consists of 200 terms. If the sum of odd terms of the GP is m , and the sum of even terms of the GP is n , then what is its common ratio?

Options

  1. Am / n
  2. Bn / m
  3. Cm+(n / m)
  4. Dn+(m / n)

Correct answer

B. n / m

Step-by-step solution

S_n= a (1-r^n ) 1-r given: a₁+a₃+ +a₁₉₉=m a [ (r^2 )¹⁰⁰-1 ] r^2-1 =m ...(1) also aligned & a₂+a₄+ +a₂₀₀=n & ar [ (r^2 )¹⁰⁰-1 ] r^2-1 =n aligned ...(2) eq. (2) (1) r= n m

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