Question

If the sum of the first n terms of an A.P. is `1/2(3n^2+7n)`, then find its nth term. Hence, write its 20th term.

Answer 1

We have, `S_(n) = (1)/(2) (3n^(2) + 7n)`.
`therefore S_(n-1) = (1)/(2) * {3(n-1)^(2) + 7(n-1)} = (1)/(2) (3n^(2) + n-4).`
`therefore T_(n) = (S_(n)-S_(n-1)) = (1)/(2) (3n^(2) +7n) = (1)/(2)(3n^(2) +n-4)`
` = (1)/(2) (6n +4) = (3n + 2)`
`therefore "nth term" = (3n +2)`
Hence, 20th term `= (3 xx 20 + 2) = 62.`