Answer:
Step-by-step explanation:
1)Since we know that recursive formula of the geometric sequence is
[tex]a_{n}=a_{n-1}*r[/tex]
so comparing it with the given recursive formula [tex]a_{n}=a_{n-1}*-4[/tex]
we get common ratio =-4
8th term= [tex]a_{1}*(r)^{n-1}=-2*(-4)^{7} =32768.[/tex]
Explicit Formula =[tex]-2*(-4)^{n-1}[/tex]
2) Comparing the given recursive formula [tex]a_{n}=a_{n-1}*-2[/tex]
with standard recursive formula [tex]a_{n}=a_{n-1}*r[/tex]
we get common ratio =-2
8th term= [tex]a_{1}*(r)^{n-1}=-4*(-2)^{7} =512.[/tex]
Explicit Formula =[tex]-4*(-2)^{n-1}[/tex]
3)Comparing the given recursive formula [tex]a_{n}=a_{n-1}*3[/tex]
with standard recursive formula [tex]a_{n}=a_{n-1}*r[/tex]
we get common ratio =3
8th term= [tex]a_{1}*(r)^{n-1}=-1*(3)^{7} =-2187.[/tex]
Explicit Formula =[tex]-1*(3)^{n-1}[/tex]
4)Comparing the given recursive formula [tex]a_{n}=a_{n-1}*-4[/tex]
with standard recursive formula [tex]a_{n}=a_{n-1}*r[/tex]
we get common ratio =-4
8th term= [tex]a_{1}*(r)^{n-1}=3*(-4)^{7} =-49152.[/tex]
Explicit Formula =[tex]3*(-4)^{n-1}[/tex]
5)Comparing the given recursive formula [tex]a_{n}=a_{n-1}*-4[/tex]
with standard recursive formula [tex]a_{n}=a_{n-1}*r[/tex]
we get common ratio =-4
8th term= [tex]a_{1}*(r)^{n-1}=-4*(-4)^{7} =65536.[/tex]
Explicit Formula =[tex]-4*(-4)^{n-1}[/tex]
6)Comparing the given recursive formula [tex]a_{n}=a_{n-1}*-2[/tex]
with standard recursive formula [tex]a_{n}=a_{n-1}*r[/tex]
we get common ratio =-2
8th term= [tex]a_{1}*(r)^{n-1}=3*(-2)^{7} =-384.[/tex]
Explicit Formula =[tex]3*(-2)^{n-1}[/tex]
7)Comparing the given recursive formula [tex]a_{n}=a_{n-1}*-5[/tex]
with standard recursive formula [tex]a_{n}=a_{n-1}*r[/tex]
we get common ratio =-5
8th term= [tex]a_{1}*(r)^{n-1}=4*(-5)^{7} =-312500.[/tex]
Explicit Formula =[tex]4*(-5)^{n-1}[/tex]
8)Comparing the given recursive formula [tex]a_{n}=a_{n-1}*-5[/tex]
with standard recursive formula [tex]a_{n}=a_{n-1}*r[/tex]
we get common ratio =-5
8th term= [tex]a_{1}*(r)^{n-1}=2*(-5)^{7} =-156250.[/tex]
Explicit Formula =[tex]2*(-5)^{n-1}[/tex]
