If sn, the sum of the first n terms of an AP, by sn=5n^2+3n, then find its its nth term. Pls ans

If sn, the sum of the first n terms of an AP, by sn=5n^2+3n, then find

1.	If sn, the sum of the first n terms of an AP, by sn=5n^2+3n, then find its its nth term. Pls ans
Answer» Let an be the n th term of the A.P. Then,an = Sn - Sn-1{tex}\\Rightarrow{/tex}\xa0an= (5n2 + 3n) - {5(n -1)2 + 3 (n- 1)}\xa0{tex}\\left[ \\begin{array} { l } { \\text { Replacing } n \\text { by } ( n - 1 ) \\text { in } S _ { n } } \\\\ { \\text { to get } S _ { n - 1 } = 5 ( n - 1 ) ^ { 2 } + 3 ( n - 1 ) } \\end{array} \\right]{/tex}{tex}\\Rightarrow{/tex}an = (5n2 + 3n) - {5(n2 - 2n+ 1) + 3n - 3}{tex}\\Rightarrow{/tex} an = (5n2 + 3n) - {5n2 -10n + 5 + 3n - 3}{tex}\\Rightarrow{/tex}\xa0an = (5n2 + 3n) - (5n2\xa0- 7n + 2){tex}\\Rightarrow{/tex}\xa0an = 10n - 2