Answer:
Sum = [tex]\frac{1364}{3}[/tex]
Step-by-step explanation:
The given geometric sequence is:
[tex]\frac{4}{3}, \frac{16}{3}, \frac{64}{3}, \frac{256}{3},\frac{1024}{3}[/tex]
The first term of the sequence is [tex]a_{1}=\frac{4}{3}[/tex]
The common ratio of the sequence is:
[tex]r=\frac{\frac{16}{3} }{\frac{4}{3} }=4[/tex]
There are 5 terms in total in the given sequence so n = 5
The formula to calculate the sum of finite geometric sequence is:
[tex]S_{n} = \frac{a_{1}(1-r^{n}) }{1-r}[/tex]
Using the given values, we get:
[tex]S_{5}=\frac{\frac{4}{3} (1-4^{5}) }{1-5} = \frac{1364}{3}[/tex]
Therefore, the sum of given geometric sequence is [tex]\frac{1364}{3}[/tex]
