Answer:
[tex]S_6=189[/tex]
Step-by-step explanation:
This is a geometric series with [tex]a_1=3[/tex] and common ratio [tex]r=2[/tex]. Using the formula [tex]\displaystyle S_n=\frac{a_1(1-r^n)}{1-r}[/tex] to find the sum of the first [tex]n=6[/tex] terms, we have:
[tex]\displaystyle S_n=\frac{a_1(1-r^n)}{1-r}\\\\S_6=\frac{3(1-2^6)}{1-2}\\\\S_6=\frac{3(1-64)}{-1}\\\\S_6=\frac{3(-63)}{-1}\\\\S_6=\frac{-189}{-1}\\\\S_6=189[/tex]
So, the given series works out to be [tex]S_6=189[/tex].
