if sn the sum of first n term and AP is given by sn =5n2+3n,then find its nth term
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Given Sn = 5n² + 3n
S( n - 1 ) = 5 ( n - 1 )² + 3 ( n - 1 )
S ( n - 1 ) = 5 ( n² - 2n + 1 ) + 3n - 3
S ( n - 1 ) = 5n² - 10n + 5 + 3n - 3
S ( n - 1 ) = 5n² - 7n + 2
To find first nth term ;
an = Sn - S ( n - 1 )
an = 5n² + 3n - ( 5n² - 7n + 2 )
an = 5n² + 3n - 5n² + 7n - 2
an = 10n - 2
S( n - 1 ) = 5 ( n - 1 )² + 3 ( n - 1 )
S ( n - 1 ) = 5 ( n² - 2n + 1 ) + 3n - 3
S ( n - 1 ) = 5n² - 10n + 5 + 3n - 3
S ( n - 1 ) = 5n² - 7n + 2
To find first nth term ;
an = Sn - S ( n - 1 )
an = 5n² + 3n - ( 5n² - 7n + 2 )
an = 5n² + 3n - 5n² + 7n - 2
an = 10n - 2
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