Respuesta :
Hello!
Let's write some important information that we know:
• a1 ,= 8,192
,• a3 ,= 512
,• q ,= ?
First, we have to discover the value of q, using the formula below:
[tex]a_n=a_1\cdot q^{n-1}[/tex]Let's replace n as 3:
[tex]\begin{gathered} 512=8,192\cdot q^{3-1} \\ 512=8,192\cdot q^2 \\ 8,192q^2=512 \\ q^2=\frac{512}{8192}=\frac{1}{16} \\ \\ q^=\sqrt{\frac{1}{16}}=\frac{\sqrt{1}}{\sqrt{16}}=\frac{1}{4} \\ \end{gathered}[/tex]So, q = 1/4.
With this information, now we are able to calculate the 10th term, using the same formula:
[tex]\begin{gathered} a_n=a_1\cdot q^{n-1} \\ a_{10}=8,192\cdot(\frac{1}{4})^{10-1} \\ \\ a_{10}=8,192\cdot(\frac{1}{4})^9 \\ \\ \boxed{\mathrm{a_{10}=\dfrac{1}{32}}=0.03125} \end{gathered}[/tex]Answer:
Alternative A. 0.03125
