In an AP the sum of 1st n term Sn=3n^2/2+5n/2 find 25th term

1.	In an AP the sum of 1st n term Sn=3n^2/2+5n/2 find 25th term
Answer» According to the question,we are given that,\xa0{tex}S _ { n } = \\frac { 3 n ^ { 2 } } { 2 } + \\frac { 5 n } { 2 } = \\frac { 3 n ^ { 2 } + 5 n } { 2 }{/tex}{tex}\\Rightarrow S _ { n - 1 } = \\frac { 3 ( n - 1 ) ^ { 2 } + 5 ( n - 1 ) } { 2 }{/tex}{tex}= \\frac { 3 \\left( n ^ { 2 } - 2 n + 1 \\right) + 5 n - 5 } { 2 }{/tex}{tex}= \\frac { 3 n ^ { 2 } - 6 n + 3 + 5 n - 5 } { 2 }{/tex}{tex}= \\frac { 3 n ^ { 2 } - n - 2 } { 2 }{/tex}Now,nth term = Tn=Sn-Sn-1={tex}= \\frac { 3 n ^ { 2 } + 5 n } { 2 } - \\frac { 3 n ^ { 2 } - n - 2 } { 2 } = \\frac { 3 n ^ { 2 } + 5 n - 3 n ^ { 2 } + n + 2 } { 2 }{/tex}={tex}\\frac{{6n + 2}}{2}{/tex}=3n+125th term=T25=3(25)+1=75+1=76.

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