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AP EAMCET201726 Apr 2017Morning ShiftMathematicsSequences and SeriesActual

The sum of first n terms of 1 2.5 + 1 5.8 + 1 8.11 + is

Options

  1. A3 n 2(3 n+2)
  2. B3 n 3 n+2
  3. Cn 2(3 n+2)
  4. Dn 3 n+2

Correct answer

C. n 2(3 n+2)

Step-by-step solution

aligned & (c) Let, S_n= 1 2 5 + 1 5 8 + 1 8 11 + . . upto n terms & = 1 3 [ 1 2 5 + 1 5 8 + 1 8 11 + . . upto n terms ] & = 1 3 [ 5-2 2 5 + 8-5 5 8 + 11-8 8 11 + . . upto n terms ] & = 1 3 [ ( 1 2 - 1 5 )+ ( 1 5 - 1 8 )+ ( 1 8 - 1 11 ) . aligned .+ ( 1 3 n-1 - 1 3 n+2 ) ] aligned & = 1 3 [ 1 2 - 1 3 n+2 ]= 1 3 [ 3 n+2-2 2(3 n+2) ] & S_n= n 2(3 n+2) aligned

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