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MHT CET202013 Oct 2020Morning ShiftMathematicsSequences and SeriesActual

For a sequence if S_ n = 5^ n -2^ n 2^ n , then its fourth term is

Options

  1. A375 16
  2. B375 8
  3. C251 8
  4. D251 16

Correct answer

A. 375 16

Step-by-step solution

s_ n = 5^ n -2^ n 2^ n ; s_ n-1 = 5^ n-1 -2^ n-1 2^ n-1 aligned T_ n &=s_ n -s_ n-1 T_ n &= 5^ n -2^ n 5^ n-1 2^ n T₄ &= 5⁴-2 5³ 2⁴ &= 625-250 16 &= 375 16 aligned

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