Answer:
[tex]\bold{a_{16} =-4^{16}=-2^{32}=-4\,294\,967\,296}[/tex]
Step-by-step explanation:
[tex]a_1=4\\a_2=-16\\a_3=64\\\\\dfrac{a_2}{a_1}=\dfrac{-16}{4}=-4\\\\ \dfrac{a_3}{a_2}=\dfrac{64}{-16}=-4\\\\\\\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=-4=r[/tex]
The formula:
[tex]a_n=a_1\cdot q^{n-1}[/tex]
Therefore:
[tex]a_{16} =4\cdot(-4)^{16-1}=4\cdot(-4)^{15}=-4^{16}=-2^{32}=-4\,294\,967\,296[/tex]
