Answer:
[tex]a_1=1.04[/tex]
Step-by-step explanation:
We have a geometric sequence with:
[tex]Sn = 89,800[/tex], [tex]r = 3.4[/tex], and [tex]n = 10[/tex]
Where
Sn is the sum of the sequence
r is the common ratio
[tex]a_1[/tex] is the first term in the sequence
n is the number of terms in the sequence
The formula to calculate the sum of a finite geometric sequence is:
[tex]S_n=\frac{a_1(1-r^n)}{1-r}[/tex]
Then:
[tex]89,800=\frac{a_1(1-(3.4)^{10})}{1-3.4}[/tex]
Now we solve for [tex]a_1[/tex]
[tex]89,800(1-3.4)=a_1(1-(3.4)^{10})[/tex]
[tex]a_1=\frac{89,800(1-3.4)}{1-(3.4)^{10}}\\\\a_1=1.04[/tex]
