Answer:
[tex]a_{10}=\dfrac{1}{128}[/tex]
Step-by-step explanation:
In the geometric series:
[tex]a_1=4\\ \\r=\dfrac{1}{2}[/tex]
The nth term of the geometric sequence can be calculated using formula
[tex]a_n=a_1\cdot r^{n-1}[/tex]
In your case, n = 10, then
[tex]a_{10}\\ \\=4\cdot \left(\dfrac{1}{2}\right)^{10-1}\\ \\=4\cdot \left(\dfrac{1}{2}\right)^9\\ \\=2^2\cdot \dfrac{1}{2^9}\\ \\=\dfrac{1}{2^{9-2}}\\ \\=\dfrac{1}{2^7}\\ \\=\dfrac{1}{128}[/tex]
