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AP EAMCET201920 Apr 2019Evening ShiftMathematicsSequences and SeriesActual

The sum of first n terms of the series 3 5 + 21 25 + 117 125 + is

Options

  1. An+ 2^ n+1 3 5^n - 2 3
  2. Bn- 2^ n+1 3 5^n - 2 3
  3. Cn+ 2^ n+1 3 5^n + 2 3
  4. Dn- 2^ n+1 3 5^n + 2 3

Correct answer

A. n+ 2^ n+1 3 5^n - 2 3

Step-by-step solution

Given, series aligned & 3 5 + 21 25 + 117 125 + + upto n terms & = (1- 2 5 )+ (1- 4 25 )+ (1- 8 125 )+ + upto aligned n terms aligned & =n- [ 2 5 + ( 2 5 )^2+ ( 2 5 )^3+ + upto n terms ] & =n- 2 5 (1- ( 2 5 )^n ) 1- 2 5 & =n- [ a+a r+a r^2+ +a r^ n-1 = a (1-r^n ) 1-r ] 3 / 5 =n+ 2^ n+1 3 5^n - 2 3 aligned Hence, option (a) is correct.

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