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The sum of the first n terms of a linear sequence is (S_{n} = n^{2}…

The sum of the first n terms of a linear sequence is (S_{n} = n^{2} + 2n). Find the common difference of the sequence.

  • A.
    5
  • B.
    4
  • C.
    3
  • D.
    2
Correct Answer: Option D
Explanation

(S_{n} = frac{n}{2}(2a + (n – 1)d )

(frac{n}{2}(2a + (n – 1) d = n^{2} + 2n)

(n(2a + (n – 1) d = 2n^{2} + 4n)

(2an + n^{2}d – nd = 2n^{2} + 4n)

Comparing the equations, d = 2 (coefficient of (n^{2})).