Answer:
Step-by-step explanation:
The formula of a sum of terms of a gometric sequence:
[tex]S_n=a_1\cdot\dfrac{1-r^n}{1-r}[/tex]
a₁ - first term
r - common ratio
We have
[tex]a_n=-4(6)^{n-1}[/tex]
Calculate a₁. Put n = 1:
[tex]a_1=-4(6)^{1-1}=-4(6)^0=-4(1)=-4[/tex]
Calculate the common ratio:
[tex]r=\dfrac{a_{n+1}}{a_n}\\\\a_{n+1}=-4(6)^{n+1-1}=-4(6)^n\\\\r=\dfrac{-4(6)^n}{-4(6)^{n-1}}=6^n:6^{n-1}\\\\\text{use}\ a^n:a^m=a^{n-m}\\\\r=6^{n-(n-1)}=6^{n-n+1}=6^1=6[/tex]
[tex]\text{Substitute}\ a_1=-4,\ n=7,\ r=6:\\\\S_7=-4\cdot\dfrac{1-6^7}{1-6}=-4\cdot\dfrac{1-279936}{-5}=-4\cdot\dfrac{-279935}{-5}=(-4)(55987)\\\\S_7=-223948[/tex]
