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COMEDK2020MathematicsSequences and Series

1 2 5 + 1 5 8 + 1 8 11 + 1 (3 n-1)(3 n+2) =

Options

  1. An 6 n+3
  2. Bn 6 n-4
  3. Cn+1 6 n+4
  4. Dn 6 n+4

Correct answer

D. n 6 n+4

Step-by-step solution

Let S_ n = 1 2 5 + 1 5 8 + 1 8 11 + aligned &= 1 3 [ 3 2 5 + 3 5 8 + 3 8 11 + + 1 (3 n-1)(3 n+2) ] &= 1 3 [ 5-2 2 5 + 8-5 5 8 + 11-8 8 11 + + (3 n+2)-(3 n-1) (3 n-1)(3 n+2) ] &= 1 3 [ 1 2 - 1 5 + 1 5 - 1 8 + 1 8 - 1 11 + + 1 3 n-1 - 1 3 n+2 ] &= 1 3 [ 1 2 - 1 3 n+2 ]= 1 3 [ 3 n+2-2 2(3 n+2) ] &= n 2(3 n+2) = n 6 n+4 aligned

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