Answer:
6th term is 0.125
Step-by-step explanation:
a1 = 128 and a3 = 8
To find nth term of geometric sequence we use formula
[tex]a_n = a_1(r)^{n-1}[/tex]
a1 is the first term
r is the common ratio
a1= 128
Given a3 = 8, n=3, a1= 128
[tex]a_n = a_1(r)^{n-1}[/tex]
[tex]a_3 = 128(r)^{3-1}[/tex]
[tex]8 = 128(r)^{2}[/tex]
Divide by 128 on both sides
1/16 = r^2
take square root on both sides
So r= 1/4
To find 6th term, replace r= 1/4
[tex]a_6 = 128(\frac{1}{4})^{6-1}[/tex]
a_6= 0.125
