3 + 13 + 29 + 51 + 79 + ... To N Terms =_____. (A) n2 + 5n3.(B) n3 + 2n2.(C) 2n2 + 7n3.(D) None Of These.

The correct answer is (C) \( 2n^{2} + 7n^{3}.\)

Let \( S_{n} \)= 3 + 13 + 29 + 51 + 79 + …… + n terms.

As given in the question:

\( S_{1}\) = 3

\( S_{2} \)= 3 + 13 = 16

\( S_{3}\) = 3 + 13 + 29 = 45

From the above-given option (C)

\( S_{n} = n^{3} + 2n^{2}\)

By taking n = 1:

\( S_{1} = 1^{3} + 2.1^{2} = 3\) \( S_{2} = 2^{3} + 2.2^{2} = 16\) \( S_{3} = 3^{3} + 2.3^{2} = 45\)

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