The sum of the first n terms of a linear sequence is (S_{n} = n^{2} + 2n). Determine the general term of the sequence.
-
A.
n + 1 -
B.
2n + 1 -
C.
3n + 1 -
D.
4n + 1
Correct Answer: Option B
Explanation
(S_{n} = 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)
(n^{2}d = 2n^{2})
(d = 2)
((2a – d) n = 4n)
(2a – d = 4 implies 2a = 4 + d = 4 + 2 = 6)
(a = 3)
(T_{n} = a + (n – 1)d)
= (3 + (n – 1)2 = 3 + 2n – 2 = 2n + 1)