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What is the n ^ th term of the sequence 25,-125,625 , -3125, ?

Options

  1. A(-5)^ 2 n -1
  2. B(-1)^ 2 n 5^ n +1
  3. C(-1)^ 2 n -1 5^ n +1
  4. D(-1)^ n -1 5^ n +1

Correct answer

D. (-1)^ n -1 5^ n +1

Step-by-step solution

Given series 25,-125,625,-3125 is geometric progression. aligned & a = t ₁=25, t ₂=-125 & r= t₂ t₁ = -125 25 =-5 & n ^ th term ( t _ n )= ar ^ n -1 & =(25)(-5)^ n -1 & =(5)^2(-1)^ n -1 (5)^ n -1 & =(-1)^ n -1 (5)^ 2+ n -1 & =(-1)^ n -1 5^ n +1 aligned

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