Answer:
[tex]a_1=2[/tex]
[tex]a_{20}=1048576[/tex]
Step-by-step explanation:
Geometric Series
The sum of the first n terms of a geometric series whose first term is a1 and a common ratio r is
[tex]\displaystyle S_n=a_1\cdot \frac{r^n-1}{r-1}[/tex]
The problem provides the following data
[tex]S_{12}=8190[/tex]
[tex]r=2[/tex]
[tex]n=12[/tex]
Replacing the values in the formula:
[tex]\displaystyle 8190=a_1\cdot \frac{2^{12}-1}{2-1}[/tex]
Operating
[tex]\displaystyle 8190=a_1\cdot 4095[/tex]
Solving for a1
[tex]a_1=8190/4095=2[/tex]
[tex]\boxed{a_1=2}[/tex]
The first term is 2
The general term of the series is
[tex]a_n=a_1.r^{n-1}[/tex]
Compute the 20th term
[tex]a_{20}=2\cdot 2^{20-1}[/tex]
[tex]\boxed{a_{20}=1048576}[/tex]
