Answer :
Considering the given Sequences let's find the explicit rule, and then the 7th element:
1) Examining it we can tell this is a Geometric Sequence
[tex]\begin{gathered} (400,\text{ 200, 100)} \\ a_n=a_1q^{n-1}\Rightarrow a_n=400_{}(\frac{1}{2})^{n-1} \\ a_7=400(\frac{1}{2})^{7-1} \\ a_7=\frac{25}{4} \end{gathered}[/tex]2) We can tell this is another Geometric Sequence whose common ratio is 5
[tex]\begin{gathered} a_n=a_1q^{n-1} \\ a_n=1(5)^{n-1} \\ a_7=5^6 \\ a_7=15625 \end{gathered}[/tex]3) Geometric Sequence whose ratio is 4, and the first term is -1:
[tex]\begin{gathered} a_n=a_1q^{n-1} \\ a_n=-1(4)^{n-1} \\ a_7=-1(4)^6 \\ a_7=-4096 \end{gathered}[/tex]Finally, the answers are:
[tex]\begin{gathered} 1)a_n=400_{}(\frac{1}{2})^{n-1} \\ a_7=\frac{25}{4} \\ 2)a_n=1(5)^{n-1} \\ a_7=15625 \\ 3)a_n=-1(4)^{n-1} \\ a_7=-4096 \end{gathered}[/tex]