If the sum of n tems of a series be `5n^2+3n`, find its nth term. Are the terms of this series in A.P.?

Explanation

Given , ` S_(n) = 5n^(2) + 3n `
` therefore S_(n-1) = 5(n-1)^(2) + 3 (n-1) = 5(n^(2) - 2n + 1) + 3(n-1) `
` = 5n^(2) - 10n + 5 + 3n - 3 = 5n^(2) - 7n + 2 `
Now , ` a_(n) = S_(n) - S_(n-1) = 10_(n-2)`
Putting 1, 2, 3 , …. we have
` a_(1) = 8 , a_(2) = 18 , a_(3) = 28 , a_(4) = 38 `, ..
Clearly , terms of the series form an A.P.