Answer:
[tex]b_{10}=2^{19}[/tex]
Step-by-step explanation:
Given the geometric sequence [tex]2,\ 8,\ 32,\ ...[/tex]
In this sequence,
[tex]b_1=2\\ \\b_2=8\\ \\b_3=32\\ \\...[/tex]
Find the common ratio r:
[tex]r=\dfrac{b_2}{b_1}=\dfrac{8}{2}=4[/tex]
or
[tex]r=\dfrac{b_3}{b_2}=\dfrac{32}{8}=4[/tex]
Use formula for the [tex]n^{th}[/tex] term:
[tex]b_n=b_1\cdot r^{n-1},[/tex]
so
[tex]b_{10}=2\cdot 4^{10-1}\\ \\b_{10}=2\cdot 4^9\\ \\b_{10}=2\cdot 2^{18}\\ \\b_{10}=2^{19}[/tex]
