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Question
If the sum of n terms of an AP is 2n2 + 3n, then write its nth term.
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Solution
Given:
\[S_n = 2 n^2 + 3n\]
\[\Rightarrow S_1 = 2 \left( 1 \right)^2 + 3\left( 1 \right)\]
\[ = 5\]
\[ S_2 = 2 \left( 2 \right)^2 + 3\left( 2 \right)\]
\[ = 14\]
\[ \therefore a_1 + a_2 = 14\]
\[ \Rightarrow 5 + a_2 = 14\]
\[ \Rightarrow a_2 = 9\]
Common difference, d = \[a_2 - a_1\] = 9 \[-\] 5 = 4
nth term = a + \[\left( n - 1 \right)d\] = 5+\[\left( n - 1 \right)\]4
= 4n+1
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