Answer:
4/3
Step-by-step explanation:
a2 = 324 and a4 = 36
second term is 324 and fourth term is 36
[tex]a_n= a_1(r)^{n-1}[/tex]
To get second term, replace n with 2
[tex]a_2= a_1(r)^{2-1}[/tex]
[tex]a_2= a_1(r)[/tex]
replace a2 with 324
[tex]324= a_1(r)[/tex] -----------> equation 1
To get fourth term , replace n with 4
[tex]a_4= a_1(r)^{4-1}[/tex]
[tex]a_4= a_1(r)^3[/tex]
Replace the value
[tex]36= a_1(r)[/tex] -----------> equation 2
divide second equation by first equation
[tex]36= a_1(r)^3[/tex] divide by [tex]324= a_1(r)[/tex]
1/9 = r^2
take square root on both sides
1/3= r
now we find a1
[tex]324= a_1(r)[/tex]
[tex]324= a_1(\frac{1}{3})[/tex]
multiply by 3 on both sides
972= a_1
So a1= 972, r= 1/3
now find out 7 term by replacing 'n' with 7
[tex]a_7= 972(\frac{1}{3})^{7-1}[/tex]
So 7th term is 4/3
