Answer:
[tex]\large\boxed{21845}[/tex]
Step-by-step explanation:
The formula of a sum of terms of a geometric sequence:
[tex]S_n=a_1\cdot\dfrac{1-r^n}{1-r}[/tex]
We have:
[tex]a_1=1,\ a_2=4,\ a_3=16\ and\ n=8[/tex]
Calculate the common ratio:
[tex]r=\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=...=\dfrac{a_{n+1}}{a_n}\\\\r=\dfrac{4}{1}=4\\\\r=\dfrac{16}{4}=4[/tex]
CORRECT :)
Substitue:
[tex]S_8=1\cdot\dfrac{1-4^8}{1-4}=\dfrac{1-65536}{-3}=\dfrac{-65535}{-3}=21845[/tex]
