Answer:
17.98
Step-by-step explanation:
We can use the sum of a finite geometric series formula(in the picture). We can start by plugging in what we have. As of now, we have the first term, 12 and by dividing a term by a previous term, we can tell that the common ratio, r is 1/3. Lastly, we can say that n is equal to 6, because we are looking for the sum of the first 6 terms. After substituting we get:
[tex]\frac{12 - 12*(\frac{1}{3})^6}{1-\frac{1}{3} }[/tex]
We can start by simplifying:
[tex]\frac{12-12(\frac{1}{729}) }{\frac{2}{3} }[/tex]
[tex]\frac{\frac{2916}{243} -\frac{4}{243} }{\frac{2}{3} }[/tex]
[tex]\frac{\frac{2912}{243} }{\frac{2}{3} }[/tex]
[tex]\frac{2912}{243}*\frac{3}{2}[/tex]
[tex]\frac{1456}{81}[/tex]
17.975308642
This can be rounded to 17.98
