Answer:
option D
[tex]a_{1}=6561 and a_{n}=\frac{1}{3}a_{n-1}[/tex]
Step-by-step explanation:
[tex]a_{3} = 729\\\\a_{4} = 243\\\\r = \frac{a_{4}}{a_{3}}\\\\r=\frac{243}{729}\\\\r=\frac{1}{3}[/tex]
Recursive rule: Next term is obtained by multiplying (1/3) wiht the previous term
[tex]a_{n}=\frac{1}{3}*a_{n-1}[/tex]
[tex]a_{3} = \frac{1}{3}*a_{2}\\\\\\729 = \frac{1}{3}*a_{2}\\\\\\729*3=a_{2}\\\\a_{2} = 2187\\\\\\[/tex]
[tex]a_{2}=\frac{1}{3}*a_{1}\\\\\\2187=\frac{1}{3}*a_{1}\\\\\\2187*3=a_{1}\\\\a_{1}=6561[/tex]
