If $S n = 2 n^{2} + 3 n$ , then d =

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Solution

$s_{n} = 2 n^{2} + 3 n T_{n} = s_{n} {- s}_{n - 1} = 2 n^{2} + 3 n - 2 {(n - 1)}^{2} - 3 (n - 1) = 2 n^{2} + 3 n - 2 n^{2} + 2 n - 2 - 3 n + 3 = 3 n - 2 + n + 3 = 4 n + 1 T_{1} = 4 + 1 = 5 T_{2} = 8 + 1 = 9 d = - T_{1} + T_{2} d = 9 - 5 = 4$

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