Question

Find the sum of the geometric sequence. 4 divided by 3, 16 divided by 3, 64 divided by 3, 256 divided by 3, 1024 divided by 3

Answer 1

Answer:

Sum = $\frac{1364}{3}$

Step-by-step explanation:

The given geometric sequence is:

$\frac{4}{3}, \frac{16}{3}, \frac{64}{3}, \frac{256}{3},\frac{1024}{3}$

The first term of the sequence is $a_{1}=\frac{4}{3}$

The common ratio of the sequence is:

$r=\frac{\frac{16}{3} }{\frac{4}{3} }=4$

There are 5 terms in total in the given sequence so n = 5

The formula to calculate the sum of finite geometric sequence is:

$S_{n} = \frac{a_{1}(1-r^{n}) }{1-r}$

Using the given values, we get:

$S_{5}=\frac{\frac{4}{3} (1-4^{5}) }{1-5} = \frac{1364}{3}$

Therefore, the sum of given geometric sequence is $\frac{1364}{3}$