Respuesta :
58.09
ExplanationTo find the sum of a finite geometric series, use the formula,
[tex]S_n=\frac{a(1-r^n)}{(1-r)}[/tex]where
[tex]\begin{gathered} a=\text{ first term} \\ r=\text{ common ratio} \\ n=\text{ number of terms} \\ S_n=sumo\text{f the firts n terms} \end{gathered}[/tex]so
Step 1
find the common ratio :
To calculate the common ratio in a geometric sequence, divide the n^th term by the (n - 1)^th term,in other words you can just divide each number from the number preceding it in the sequence
[tex]coomin\text{ ratio =}\frac{n\text{ term }}{(n-1)\text{ term}}[/tex]so
[tex]common\text{ ratio=}\frac{\frac{28}{5}}{\frac{14}{1}}=\frac{28}{70}=0.4[/tex]so r= 0.4
Step 2
Now we can use the formula
a)
let
[tex]\begin{gathered} r=0.4 \\ n=\text{ 6} \\ a=35 \end{gathered}[/tex]b) finally, replace in the formula
[tex]\begin{gathered} S_n=\frac{a(1-r^n)}{(1-r)} \\ S_n=\frac{35(1-0.4^6)}{(1-0.4)} \\ Sn=35*1.62984 \\ Sn=58.0944\text{ } \\ rounded \\ S_n=58.09 \end{gathered}[/tex]therefore, the answer is
58.09
I hope this helps you
