Answer :
Answer:
The sum of the given geometric series is:
170.5
Step-by-step explanation:
We know that for any geometric series have 'n' terms with first terms as: ''a'' and common ratio of the terms in the series as: 'r'
We get the sum of the series by the formula :
[tex]S_n=a\times (\dfrac{r^n-1}{r-1})[/tex]
From the question we have:
a=1/2 , r=4 ( Since each term is the series is 4 times it's preceding term) and n=5 (as there are five terms in the series )
Hence, the sum of the series is:
[tex]S_5=\dfrac{1}{2}\times (\dfrac{4^5-1}{4-1})\\\\\\S_5=\dfrac{1}{2}\times (\dfrac{1023}{3})\\\\\\S_5=170.5[/tex]
Hence, the sum of the series is: 170.5