A geometric series is the sum of the terms in a geometric sequence. The formula for the sum of the first n terms of a geometric sequence is represented as:
[tex]S_n=\frac{a(1-r^n)}{1-r}[/tex]Where:
a = 4
r = 4
n = 6
Substitute the values:
[tex]S=\frac{4(1-4^6)}{1-4}[/tex]Simplify:
[tex]S=\frac{4(1-4096)}{1-4}=\frac{4(-4095)}{-3}=\frac{-16380}{-3}=5460[/tex]Answer: 5460
