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JEE Advanced2009MathematicsSequences and SeriesActual

If the sum of first n terms of an AP is cn ^2 , then the sum of squares of these n terms is

Options

  1. An (4 n^2-1 ) c^2 6
  2. Bn (4 n^2+1 ) c^2 3
  3. Cn (4 n^2-1 ) c^2 3
  4. Dn (4 n^2+1 ) c^2 6

Correct answer

C. n (4 n^2-1 ) c^2 3

Step-by-step solution

Let S_n=c^2 aligned & S_ n-1 =c(n-1)^2=c n^2+c-2 c n & T_n=2 c n-c ( T_n=S_n-S_ n-1 ) & T_n^2=(2 c n-c)^2=4 c^2 n^2+c^2-4 c^2 n & Sum = T_n^2= 4 c^2 n(n+1)(2 n+1) 6 & = 2 c^2 n(n+1)(2 n+1)+3 n c^2-6 c^2 n(n+1) 3 & = n c^2 [4 n^2+6 n+2+3-6 n-6 ] 3 & = n c^2 (4 n^2-1 ) 3 aligned

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