If Sn, the sum of first n terms of an AP, is given by Sn = 5n? + 3n, then find its nth term.

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Solution

$D e a r s t u d e n t, A s s u m i n g t h e q u e s t i o n : S_{n} = 5 n^{2} + 3 n S_{1} = a = 5 \times 1^{2} + 3 \times 1 = 8 S_{2} = 5 \times 2^{2} + 3 \times 2 = 20 + 6 = 26 a_{2} + a = 26 a_{2} = 26 - 8 = 18 d = a_{2} - a = 18 - 8 = 10 a_{n} = a + (n - 1) d = 8 + (n - 1) 10 = 8 + 10 n - 10 = 10 n - 2 R e g a r d s$

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