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in an AP, the sum of first n terms is 3n²/2 +5n/2 , find its 25th term

$given S_{n} = \frac{3 n^{2}}{2} + \frac{5 n}{2} \Rightarrow S_{n - 1} = \frac{3 (n - 1)^{2} + 5 (n - 1)}{2} \Rightarrow S_{n - 1} = \frac{3 n^{2} - 6 n + 3 + 5 n - 5}{2} \Rightarrow S_{n - 1} = \frac{3 n^{2} - n - 2}{2} we know that T_{n} = S_{n} - S_{n - 1} \Rightarrow T_{n} = \frac{3 n^{2} + 5 n - 3 n^{2} + n + 2}{2} \Rightarrow T_{n} = \frac{6 n + 2}{2} \Rightarrow T_{n} = 3 n + 1 \Rightarrow T_{25} = 3 (25) + 1 \Rightarrow T_{25} = 75 + 1 \Rightarrow T_{25} = 76$

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