[tex]\text{Sum to n terms of geometric series: } S_n = \frac{a(r^{n} - 1)}{r - 1}}, r \neq 1[/tex]
We know that a is equal to the first term, r represents the common ratio, and n represents the number of terms.
a = -4
n = 6
To find r:
[tex]\frac{-16}{-4} = \frac{-64}{-16}[/tex]
Since we do have a common ratio of 4, then we know it is a geometric sequence. Substituting everything in, we get:
[tex]S_6 = \frac{-4(4^{6} - 1)}{4 - 1}[/tex]
[tex]S_6 = \frac{-4(4096 - 1)}{3}[/tex]
[tex]S_6 = \frac{-4(4095)}{3}[/tex]
By calculator, we get:
[tex]S_6 = -5460[/tex]
