Find S8 for the geometric series 3 + -6 + 12 + -24 +…?

For the geometric series 3 + (-6) + 12 + (-24) + ……
The first term, a = 3
The common factor, r = -2

S(8)
= a (1 - r⁸) / (1 - r)
= 3 [1 - (-2)⁸] / [1 - (-2)]
= 3 × (-255) / 3
= -255

S(8) = (3 + -6) + (12 + -24) + 16((3 + -6) + (12 + -24) )
S(8) = -3 + -12 + -48 + -192
S(8) = -255

3 + -6 + 12 + -24 +…
Here first term, a =3 and
common ratio, r = -6/3=-2
hence S8 =a(r^8 -1)/(r-1)= 3{(-2)^8 -1}/{(-2-1)
= 3{256-1)(-3) = -255

a = 3, r = -6/3 = -2

|r| = |-2| = 2 > 0
Sn = a(r^n - 1)/(r - 1)
S_8 = 3((-2)^8 - 1)/(-2 - 1)
= -255

3, - 6, 12, -24, ...
an = -3 (-1)^n 2^(n - 1)
3 - 6 + 12 - 24 + 48 - 96 + 192 - 384
= 255 - 510
= -255

S_n = ( a_1 ) [ 1 - r^(n+1) ] / [ 1 - r ]