Answer: [tex]\ a_{n}=3(-3)^{n-1}[/tex]
Step-by-step explanation:
Given: A geometric sequence with its first term [tex]a_1=a=3[/tex]
and second term [tex]a_2=-9[/tex]
We know that the common ratio in of a geometric sequence=[tex]\frac{a_{n}}{a_{n-1}}[/tex]
Thus, common ratio [tex]r=\frac{-9}{3}=-3[/tex]
We know that the explicit rule for geometric sequence is written as
[tex]a_{n}=ar^{n-1}\\\Rightarrow\ a_{n}=3(-3)^{n-1}..[\text{by substituting the values of 'a' and 'r' in it }][/tex]
Thus, the explicit rule for the given geometric sequence is [tex]\ a_{n}=3(-3)^{n-1}[/tex] for every n ,a natural number.
