Answer:
the 7th term of the geometric sequence is 1/4 or 0.25
Step-by-step explanation:
Given geometric sequence terms
a1 = 1,024 and a4 = −16
nth term of geometric sequence is
[tex]a_n= a_1(r)^{n-1}[/tex]
a1 = 1,024 and a4 = −16
Plug in 4 for n and solve for 'r'
[tex]a_4= a_1(r)^{4-1}[/tex]
[tex]-16= 1024(r)^{3}[/tex]
Divide both sides by 1024
[tex]\frac{-1}{64} = r^3[/tex]
Now take cube root on both sides
[tex]\frac{-1}{4} = r[/tex]
To find 7th term we plug in n=7 , r= -1/4 , a1 = 1024
[tex]a_n= a_1(r)^{n-1}[/tex]
[tex]a_7= 1024(-1/4)^{7-1}[/tex]
[tex]a_7= 1024(-1/4)^{6}[/tex]
a_7 = 0.25
