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Question
If the sum of n terms of an A.P. is 2 n2 + 5 n, then its nth term is
Options
4n − 3
3 n − 4
4 n + 3
3 n + 4
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Solution
4n +3
\[S_n = 2 n^2 + 5n\]
\[ S_1 = 2 . 1^2 + 5 . 1 = 7\]
\[ \therefore a_1 = 7\]
\[ S_n = 2 . 2^2 + 5 . 2 = 18\]
\[ \therefore a_1 + a_2 = 18\]
\[ \Rightarrow a_2 = 11\]
\[\text { Common difference, } d = 11 - 7 = 4\]
\[ a_n = a + \left( n - 1 \right)d\]
\[ = 7 + \left( n - 1 \right)4\]
\[ = 4n + 3\]
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