Answer:
The sum is [tex]9,331[/tex]
Step-by-step explanation:
we have
[tex]1,6,36,...[/tex]
we have
[tex]a1=1[/tex]
[tex]a2=6[/tex]
[tex]a3=36[/tex]
Find the common ratio r
[tex]a2/a1=6/1=6[/tex]
[tex]a3/a2=36/6=6[/tex]
The common ratio is r=6
The formula to calculate the sum in a geometric sequence is equal to
[tex]S=a1\frac{(1-r^{n})}{(1-r)}[/tex]
where
n is the number of terms
r is the common ratio
a1 is the first term
we have
[tex]n=6[/tex]
[tex]a1=1[/tex]
[tex]r=6[/tex]
substitute
[tex]S=(1)\frac{(1-(6)^{6})}{(1-6)}[/tex]
[tex]S=\frac{(1-(6)^{6})}{(-5)}[/tex]
[tex]S=9,331[/tex]
