Question

The sum of the first n terms of an arithmetic series is 2n(n+3).

Find the first term of the series using the formula n/2(2a+(n-1)d)

Answer 1

Sum:

`{ \bf{S _(n) = (n)/(2) (2a + (n - 1)d) }} \\ \\ { \sf{2n(n + 3) = (n)/(2)(2a + (n - 1)d) }} \\ \\ { \sf{4 {n} + 12=2a + (n - 1)d }} \\ { \sf{2a = 4n - nd + d + 12}} \\ { \sf{2a = n(4 - d) + 12 + d}} \\ { \sf{a = (1)/(2)(n(4 - d) + 12 + d) }}`