Calculate the sum of n terms of the string An = n^2 + 12n.

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We have to find the sum of the terms An = n^2 + 12n

Now Sum [ An], of n terms

=> Sum [ n^2 + 12n ] , of n terms

=> Sum [ n^2] + Sum [ 12n] , of n terms

=> n(n+1)(2n+1)/6 + 12* n(n+1)/2

=>...

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We have to find the sum of the terms An = n^2 + 12n

Now Sum [ An], of n terms

=> Sum [ n^2 + 12n ] , of n terms

=> Sum [ n^2] + Sum [ 12n] , of n terms

=> n(n+1)(2n+1)/6 + 12* n(n+1)/2

=> n(n+1)(2n+1)/6 + 6*n(n+1)

=> n(n+1) [ (2n+1)/6 + 6]

=> n(n+1)[ (2n + 1 + 36)/6)]

=> n(n+1)(2n + 37)/ 6

=> (1/6)*n*(n+1)*(2n+ 37)

The required sum is (1/6)*n*(n+1)*(2n+ 37)

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