求n和首n項之和

1458, 486, 162, 54, … , 2

This is a geometric sequence

First term, a = 1458

Common ratio, r = 486 / 1458 = 1 / 3

So, the nth term, Tn = 2

1458(1 / 3)n-1 = 2

(2 X 36) / 3n-1 = 2

2 / 3n-7 = 2

1 = 3n-7

30 = 3n-7

n = 7

Sn = S7

= 1458[1 – (1/3)7] / (1 – 1/3)

= 2186

a=1458 r=1/3
ar^(n-1)=2
(1/3)^(n-1)= 2/1458
n-1=6
n=7

首n項之和
a (1 - r^n)/(1 - r)=1458(1- (1/3)^7)/(1-(1/3))=2186