超易的geometric squence(5點分)

Sn = a x [1 + R + (R^2) + ... + (R^n)]
R x Sn = a x {R + (R^2) + (R^3) + ... + [R^(n+1)]}

so,

Sn - (R x Sn) = a x {1 - [R^(n+1)]}
(1 - R) x Sn = a x {1 - [R^(n+1)]}
Sn = a x {1 - [R^(n+1)]} / (1 - R)

a = first term of geometric series = 3
R = common ratio = 2√3

the sixth term = a x [R^(6-1)] = a x (R^5) = 3 x [(2√3)^5] = 3 x (32√243) = 3 x [32√(81x3)] = 3 x 32 x 9 x √3 = 864√3

Let the sixth term be T6

First term, a = 3
Common ratio, r = 2√3

T6
= ar^(6-1)
= (3)(2√3)^5
= (3)(2^5)[(√3)^5]
= (3)(32)(9√3)
= 864√3//