Answer:
Step-by-step explanation:
1)Since we know that recursive formula of the geometric sequence is
![a_{n}=a_{n-1}*r](https://tex.z-dn.net/?f=a_%7Bn%7D%3Da_%7Bn-1%7D%2Ar)
so comparing it with the given recursive formula ![a_{n}=a_{n-1}*-4](https://tex.z-dn.net/?f=a_%7Bn%7D%3Da_%7Bn-1%7D%2A-4)
we get common ratio =-4
8th term= ![a_{1}*(r)^{n-1}=-2*(-4)^{7} =32768.](https://tex.z-dn.net/?f=a_%7B1%7D%2A%28r%29%5E%7Bn-1%7D%3D-2%2A%28-4%29%5E%7B7%7D%20%3D32768.)
Explicit Formula =![-2*(-4)^{n-1}](https://tex.z-dn.net/?f=-2%2A%28-4%29%5E%7Bn-1%7D)
2) Comparing the given recursive formula
with standard recursive formula ![a_{n}=a_{n-1}*r](https://tex.z-dn.net/?f=a_%7Bn%7D%3Da_%7Bn-1%7D%2Ar)
we get common ratio =-2
8th term= ![a_{1}*(r)^{n-1}=-4*(-2)^{7} =512.](https://tex.z-dn.net/?f=a_%7B1%7D%2A%28r%29%5E%7Bn-1%7D%3D-4%2A%28-2%29%5E%7B7%7D%20%3D512.)
Explicit Formula =![-4*(-2)^{n-1}](https://tex.z-dn.net/?f=-4%2A%28-2%29%5E%7Bn-1%7D)
3)Comparing the given recursive formula
with standard recursive formula ![a_{n}=a_{n-1}*r](https://tex.z-dn.net/?f=a_%7Bn%7D%3Da_%7Bn-1%7D%2Ar)
we get common ratio =3
8th term= ![a_{1}*(r)^{n-1}=-1*(3)^{7} =-2187.](https://tex.z-dn.net/?f=a_%7B1%7D%2A%28r%29%5E%7Bn-1%7D%3D-1%2A%283%29%5E%7B7%7D%20%3D-2187.)
Explicit Formula =![-1*(3)^{n-1}](https://tex.z-dn.net/?f=-1%2A%283%29%5E%7Bn-1%7D)
4)Comparing the given recursive formula
with standard recursive formula ![a_{n}=a_{n-1}*r](https://tex.z-dn.net/?f=a_%7Bn%7D%3Da_%7Bn-1%7D%2Ar)
we get common ratio =-4
8th term= ![a_{1}*(r)^{n-1}=3*(-4)^{7} =-49152.](https://tex.z-dn.net/?f=a_%7B1%7D%2A%28r%29%5E%7Bn-1%7D%3D3%2A%28-4%29%5E%7B7%7D%20%3D-49152.)
Explicit Formula =![3*(-4)^{n-1}](https://tex.z-dn.net/?f=3%2A%28-4%29%5E%7Bn-1%7D)
5)Comparing the given recursive formula
with standard recursive formula ![a_{n}=a_{n-1}*r](https://tex.z-dn.net/?f=a_%7Bn%7D%3Da_%7Bn-1%7D%2Ar)
we get common ratio =-4
8th term= ![a_{1}*(r)^{n-1}=-4*(-4)^{7} =65536.](https://tex.z-dn.net/?f=a_%7B1%7D%2A%28r%29%5E%7Bn-1%7D%3D-4%2A%28-4%29%5E%7B7%7D%20%3D65536.)
Explicit Formula =![-4*(-4)^{n-1}](https://tex.z-dn.net/?f=-4%2A%28-4%29%5E%7Bn-1%7D)
6)Comparing the given recursive formula
with standard recursive formula ![a_{n}=a_{n-1}*r](https://tex.z-dn.net/?f=a_%7Bn%7D%3Da_%7Bn-1%7D%2Ar)
we get common ratio =-2
8th term= ![a_{1}*(r)^{n-1}=3*(-2)^{7} =-384.](https://tex.z-dn.net/?f=a_%7B1%7D%2A%28r%29%5E%7Bn-1%7D%3D3%2A%28-2%29%5E%7B7%7D%20%3D-384.)
Explicit Formula =![3*(-2)^{n-1}](https://tex.z-dn.net/?f=3%2A%28-2%29%5E%7Bn-1%7D)
7)Comparing the given recursive formula
with standard recursive formula ![a_{n}=a_{n-1}*r](https://tex.z-dn.net/?f=a_%7Bn%7D%3Da_%7Bn-1%7D%2Ar)
we get common ratio =-5
8th term= ![a_{1}*(r)^{n-1}=4*(-5)^{7} =-312500.](https://tex.z-dn.net/?f=a_%7B1%7D%2A%28r%29%5E%7Bn-1%7D%3D4%2A%28-5%29%5E%7B7%7D%20%3D-312500.)
Explicit Formula =![4*(-5)^{n-1}](https://tex.z-dn.net/?f=4%2A%28-5%29%5E%7Bn-1%7D)
8)Comparing the given recursive formula
with standard recursive formula ![a_{n}=a_{n-1}*r](https://tex.z-dn.net/?f=a_%7Bn%7D%3Da_%7Bn-1%7D%2Ar)
we get common ratio =-5
8th term= ![a_{1}*(r)^{n-1}=2*(-5)^{7} =-156250.](https://tex.z-dn.net/?f=a_%7B1%7D%2A%28r%29%5E%7Bn-1%7D%3D2%2A%28-5%29%5E%7B7%7D%20%3D-156250.)
Explicit Formula =![2*(-5)^{n-1}](https://tex.z-dn.net/?f=2%2A%28-5%29%5E%7Bn-1%7D)