Answer:
The sum of the geometric series = 11.93
Explanation:
The sum of the first n terms of a geometric series is:
[tex]S_n=\frac{a(1-r^n)}{1-r}[/tex]
From the given expression:
The first term, a = 3
The common ratio, r = 3/4 = 0.75
The number of terms, n = 18
Substitute the given values into the formula above
[tex]\begin{gathered} S_{18}=\frac{3(1-0.75^{18})}{1-0.75} \\ \\ S_{18}=\frac{3(1-0.00563771011)}{0.25} \\ \\ S_{18}=\frac{2.98308686966}{0.25} \\ \\ S_{18}=11.93 \\ \end{gathered}[/tex]
The sum of the geometric series = 11.93
